http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=Aboyd33Physics Book - User contributions [en]2026-05-13T21:55:02ZUser contributionsMediaWiki 1.42.7http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=17183Biot-Savart Law2015-12-06T00:13:06Z<p>Aboyd33: </p>
<hr />
<div>[[File:Knight2_33.f.14.png|400px|thumb|right|Magnetic field of a current carrying wire, a visual of a derivation of the Biot-Savart Law for currents. [http://www4.uwsp.edu/physastr/kmenning/Phys250/Lect19.html]]]The Biot-Savart (pronounced bee-yo sahv-ar) Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law[http://dev.physicslab.org/document.aspx?doctype=3&filename=magnetism_biotsavartlaw.xml], and states that the magnetic field decreases with the square of a distance from a point of current. It is one of the most difficult of four electromagnetic equations, and is consistent with Ampere's Law and Gauss's Law for magnetism. It is so named for Jean-Baptiste Biot and Felix Savart who discovered the law in 1820.<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
An electron is located at the origin and moving at <math> 2e8 </math> m/s in the +x direction. What is the magnetic field at <math> <200, -300, 0> </math> m?<br />
<br />
First, we need to find <math> \vec r </math>, which in this case is just <math> \vec r = <200, -300, 0> </math> m. From that, we can calculate <math> \hat r </math>:<br />
<math> \hat r = \frac{ <200, -300, 0> }{\sqrt {200^2 + -300^2}}= <0.554, -0.832, 0> </math><br />
<br />
Next, we need to calculate <math> q \vec v </math>. Since we're dealing with an electron, our charge will be negative: <math> -1.6e-19* <2e8, 0, 0> = <-3.2e-11, 0, 0> </math>.<br />
Now for the cross product, <math> q\vec v\times\hat r </math>. The cross product is given as <math> \vec A\times\vec B = < AxBz - AzBy, AzBx - AxBz, AxBy-AyBz> </math>, so by using that formula we get <math> <0, 0, 2.65e-11> </math>. <br />
<br />
Finally, we can divide by the magnitude of <math> \vec r </math> squared: <math> \frac{ <0, 0, 2.65e-11> }{360.55} = <0, 0, 7.34e-14> </math>. Multiply by the constants and our final answer is <math> \vec B = <0, 0, 7.34e-21> Teslas </math><br />
<br />
===Example 2===<br />
A proton is located on the +x axis and is moving at a speed <math> \vec v </math> in the -y direction. What is the magnitude of the magnetic field at <math> <0, 0, z> </math> at <math> \theta = 34 </math> degrees?<br />
<br />
Like before, we need to find <math> \vec r </math>, and then the magnitude. <math> \vec r = <0, 0, z> - < x, 0, 0> = <-x, 0, z> </math>. The magnitude is then <math> \sqrt{x^2 + z^2} </math>. <br />
We can then multiply the magnitudes of <math> q </math> and <math>\vec v </math> to get the final answer:<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{qvsin(34)}{(\sqrt{x^2 + z^2})^2} </math><br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance] [[File:Vortex.jpg|200px|thumb|right|In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.]]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
<br />
<br />
<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
Right hand rule [[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]]<br />
Jean-Baptiste Biot [[http://www.physicsbook.gatech.edu/Jean-Baptiste_Biot]].<br />
<br />
===External links===<br />
<br />
"Teach Engineering" on Biot-Savart [https://www.teachengineering.org/view_lesson.php?url=collection/van_/lessons/van_mri_lesson_5/van_mri_lesson_5.xml]<br />
Derivation and Examples [http://study.com/academy/lesson/the-biot-savart-law-derivation-examples.html]<br />
Biot-Savart and Ampere's Law on MIT OpenCourse [http://ocw.mit.edu/high-school/physics/exam-prep/magnetic-fields/biot-savarts-law-amperes-law/]<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=17148Biot-Savart Law2015-12-06T00:10:25Z<p>Aboyd33: </p>
<hr />
<div>[[File:Knight2_33.f.14.png|400px|thumb|right|Magnetic field of a current carrying wire, a visual of a derivation of the Biot-Savart Law for currents. [http://www4.uwsp.edu/physastr/kmenning/Phys250/Lect19.html]]]The Biot-Savart (pronounced bee-yo sahv-ar) Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law[http://dev.physicslab.org/document.aspx?doctype=3&filename=magnetism_biotsavartlaw.xml], and states that the magnetic field decreases with the square of a distance from a point of current. It is one of the most difficult of four electromagnetic equations, and is consistent with Ampere's Law and Gauss's Law for magnetism. It is so named for Jean-Baptiste Biot and Felix Savart who discovered the law in 1820.Page in progress by Andrea Boyd.<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
An electron is located at the origin and moving at <math> 2e8 </math> m/s in the +x direction. What is the magnetic field at <math> <200, -300, 0> </math> m?<br />
<br />
First, we need to find <math> \vec r </math>, which in this case is just <math> \vec r = <200, -300, 0> </math> m. From that, we can calculate <math> \hat r </math>:<br />
<math> \hat r = \frac{ <200, -300, 0> }{\sqrt {200^2 + -300^2}}= <0.554, -0.832, 0> </math><br />
<br />
Next, we need to calculate <math> q \vec v </math>. Since we're dealing with an electron, our charge will be negative: <math> -1.6e-19* <2e8, 0, 0> = <-3.2e-11, 0, 0> </math>.<br />
Now for the cross product, <math> q\vec v\times\hat r </math>. The cross product is given as <math> \vec A\times\vec B = < AxBz - AzBy, AzBx - AxBz, AxBy-AyBz> </math>, so by using that formula we get <math> <0, 0, 2.65e-11> </math>. <br />
<br />
Finally, we can divide by the magnitude of <math> \vec r </math> squared: <math> \frac{ <0, 0, 2.65e-11> }{360.55} = <0, 0, 7.34e-14> </math>. Multiply by the constants and our final answer is <math> \vec B = <0, 0, 7.34e-21> Teslas </math><br />
<br />
===Example 2===<br />
A proton is located on the +x axis and is moving at a speed <math> \vec v </math> in the -y direction. What is the magnitude of the magnetic field at <math> <0, 0, z> </math> at <math> \theta = 34 </math> degrees?<br />
<br />
Like before, we need to find <math> \vec r </math>, and then the magnitude. <math> \vec r = <0, 0, z> - < x, 0, 0> = <-x, 0, z> </math>. The magnitude is then <math> \sqrt{x^2 + z^2} </math>. <br />
We can then multiply the magnitudes of <math> q </math> and <math>\vec v </math> to get the final answer:<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{qvsin(34)}{(\sqrt{x^2 + z^2})^2} </math><br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance] [[File:Vortex.jpg|200px|thumb|right|In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.]]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
<br />
<br />
<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
Right hand rule [[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]]<br />
Jean-Baptiste Biot [[http://www.physicsbook.gatech.edu/Jean-Baptiste_Biot]].<br />
<br />
===External links===<br />
<br />
"Teach Engineering" on Biot-Savart [https://www.teachengineering.org/view_lesson.php?url=collection/van_/lessons/van_mri_lesson_5/van_mri_lesson_5.xml]<br />
Derivation and Examples [http://study.com/academy/lesson/the-biot-savart-law-derivation-examples.html]<br />
Biot-Savart and Ampere's Law on MIT OpenCourse [http://ocw.mit.edu/high-school/physics/exam-prep/magnetic-fields/biot-savarts-law-amperes-law/]<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=17127Biot-Savart Law2015-12-06T00:09:10Z<p>Aboyd33: </p>
<hr />
<div>[[File:Knight2_33.f.14.png|200px|thumb|right|Magnetic field of a current carrying wire. [http://www4.uwsp.edu/physastr/kmenning/Phys250/Lect19.html]]]The Biot-Savart (pronounced bee-yo sahv-ar) Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law[http://dev.physicslab.org/document.aspx?doctype=3&filename=magnetism_biotsavartlaw.xml], and states that the magnetic field decreases with the square of a distance from a point of current. It is one of the most difficult of four electromagnetic equations, and is consistent with Ampere's Law and Gauss's Law for magnetism. It is so named for Jean-Baptiste Biot and Felix Savart who discovered the law in 1820.Page in progress by Andrea Boyd.<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
An electron is located at the origin and moving at <math> 2e8 </math> m/s in the +x direction. What is the magnetic field at <math> <200, -300, 0> </math> m?<br />
<br />
First, we need to find <math> \vec r </math>, which in this case is just <math> \vec r = <200, -300, 0> </math> m. From that, we can calculate <math> \hat r </math>:<br />
<math> \hat r = \frac{ <200, -300, 0> }{\sqrt {200^2 + -300^2}}= <0.554, -0.832, 0> </math><br />
<br />
Next, we need to calculate <math> q \vec v </math>. Since we're dealing with an electron, our charge will be negative: <math> -1.6e-19* <2e8, 0, 0> = <-3.2e-11, 0, 0> </math>.<br />
Now for the cross product, <math> q\vec v\times\hat r </math>. The cross product is given as <math> \vec A\times\vec B = < AxBz - AzBy, AzBx - AxBz, AxBy-AyBz> </math>, so by using that formula we get <math> <0, 0, 2.65e-11> </math>. <br />
<br />
Finally, we can divide by the magnitude of <math> \vec r </math> squared: <math> \frac{ <0, 0, 2.65e-11> }{360.55} = <0, 0, 7.34e-14> </math>. Multiply by the constants and our final answer is <math> \vec B = <0, 0, 7.34e-21> Teslas </math><br />
<br />
===Example 2===<br />
A proton is located on the +x axis and is moving at a speed <math> \vec v </math> in the -y direction. What is the magnitude of the magnetic field at <math> <0, 0, z> </math> at <math> \theta = 34 </math> degrees?<br />
<br />
Like before, we need to find <math> \vec r </math>, and then the magnitude. <math> \vec r = <0, 0, z> - < x, 0, 0> = <-x, 0, z> </math>. The magnitude is then <math> \sqrt{x^2 + z^2} </math>. <br />
We can then multiply the magnitudes of <math> q </math> and <math>\vec v </math> to get the final answer:<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{qvsin(34)}{(\sqrt{x^2 + z^2})^2} </math><br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance] [[File:Vortex.jpg|200px|thumb|right|In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.]]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
<br />
<br />
<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
Right hand rule [[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]]<br />
Jean-Baptiste Biot [[http://www.physicsbook.gatech.edu/Jean-Baptiste_Biot]].<br />
<br />
===External links===<br />
<br />
"Teach Engineering" on Biot-Savart [https://www.teachengineering.org/view_lesson.php?url=collection/van_/lessons/van_mri_lesson_5/van_mri_lesson_5.xml]<br />
Derivation and Examples [http://study.com/academy/lesson/the-biot-savart-law-derivation-examples.html]<br />
Biot-Savart and Ampere's Law on MIT OpenCourse [http://ocw.mit.edu/high-school/physics/exam-prep/magnetic-fields/biot-savarts-law-amperes-law/]<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=File:Knight2_33.f.14.png&diff=17082File:Knight2 33.f.14.png2015-12-06T00:03:45Z<p>Aboyd33: Biot-Savart LAw</p>
<hr />
<div>Biot-Savart LAw</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=17028Biot-Savart Law2015-12-05T23:59:04Z<p>Aboyd33: </p>
<hr />
<div>The Biot-Savart (pronounced bee-yo sahv-ar) Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law[http://dev.physicslab.org/document.aspx?doctype=3&filename=magnetism_biotsavartlaw.xml], and states that the magnetic field decreases with the square of a distance from a point of current. It is one of the most difficult of four electromagnetic equations, and is consistent with Ampere's Law and Gauss's Law for magnetism. It is so named for Jean-Baptiste Biot and Felix Savart who discovered the law in 1820. Page in progress by Andrea Boyd.<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
An electron is located at the origin and moving at <math> 2e8 </math> m/s in the +x direction. What is the magnetic field at <math> <200, -300, 0> </math> m?<br />
<br />
First, we need to find <math> \vec r </math>, which in this case is just <math> \vec r = <200, -300, 0> </math> m. From that, we can calculate <math> \hat r </math>:<br />
<math> \hat r = \frac{ <200, -300, 0> }{\sqrt {200^2 + -300^2}}= <0.554, -0.832, 0> </math><br />
<br />
Next, we need to calculate <math> q \vec v </math>. Since we're dealing with an electron, our charge will be negative: <math> -1.6e-19* <2e8, 0, 0> = <-3.2e-11, 0, 0> </math>.<br />
Now for the cross product, <math> q\vec v\times\hat r </math>. The cross product is given as <math> \vec A\times\vec B = < AxBz - AzBy, AzBx - AxBz, AxBy-AyBz> </math>, so by using that formula we get <math> <0, 0, 2.65e-11> </math>. <br />
<br />
Finally, we can divide by the magnitude of <math> \vec r </math> squared: <math> \frac{ <0, 0, 2.65e-11> }{360.55} = <0, 0, 7.34e-14> </math>. Multiply by the constants and our final answer is <math> \vec B = <0, 0, 7.34e-21> Teslas </math><br />
<br />
===Example 2===<br />
A proton is located on the +x axis and is moving at a speed <math> \vec v </math> in the -y direction. What is the magnitude of the magnetic field at <math> <0, 0, z> </math> at <math> \theta = 34 </math> degrees?<br />
<br />
Like before, we need to find <math> \vec r </math>, and then the magnitude. <math> \vec r = <0, 0, z> - < x, 0, 0> = <-x, 0, z> </math>. The magnitude is then <math> \sqrt{x^2 + z^2} </math>. <br />
We can then multiply the magnitudes of <math> q </math> and <math>\vec v </math> to get the final answer:<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{qvsin(34)}{(\sqrt{x^2 + z^2})^2} </math><br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
Right hand rule [[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]]<br />
Jean-Baptiste Biot [[http://www.physicsbook.gatech.edu/Jean-Baptiste_Biot]].<br />
<br />
===External links===<br />
<br />
"Teach Engineering" on Biot-Savart [https://www.teachengineering.org/view_lesson.php?url=collection/van_/lessons/van_mri_lesson_5/van_mri_lesson_5.xml]<br />
Derivation and Examples [http://study.com/academy/lesson/the-biot-savart-law-derivation-examples.html]<br />
Biot-Savart and Ampere's Law on MIT OpenCourse [http://ocw.mit.edu/high-school/physics/exam-prep/magnetic-fields/biot-savarts-law-amperes-law/]<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=16989Biot-Savart Law2015-12-05T23:56:21Z<p>Aboyd33: </p>
<hr />
<div>The Biot-Savart (pronounced bee-yoo sahv-ar) Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current. It is one of the most difficult is consistent with Ampere's Law and Gauss's Law for magnetism. Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
An electron is located at the origin and moving at <math> 2e8 </math> m/s in the +x direction. What is the magnetic field at <math> <200, -300, 0> </math> m?<br />
<br />
First, we need to find <math> \vec r </math>, which in this case is just <math> \vec r = <200, -300, 0> </math> m. From that, we can calculate <math> \hat r </math>:<br />
<math> \hat r = \frac{ <200, -300, 0> }{\sqrt {200^2 + -300^2}}= <0.554, -0.832, 0> </math><br />
<br />
Next, we need to calculate <math> q \vec v </math>. Since we're dealing with an electron, our charge will be negative: <math> -1.6e-19* <2e8, 0, 0> = <-3.2e-11, 0, 0> </math>.<br />
Now for the cross product, <math> q\vec v\times\hat r </math>. The cross product is given as <math> \vec A\times\vec B = < AxBz - AzBy, AzBx - AxBz, AxBy-AyBz> </math>, so by using that formula we get <math> <0, 0, 2.65e-11> </math>. <br />
<br />
Finally, we can divide by the magnitude of <math> \vec r </math> squared: <math> \frac{ <0, 0, 2.65e-11> }{360.55} = <0, 0, 7.34e-14> </math>. Multiply by the constants and our final answer is <math> \vec B = <0, 0, 7.34e-21> Teslas </math><br />
<br />
===Example 2===<br />
A proton is located on the +x axis and is moving at a speed <math> \vec v </math> in the -y direction. What is the magnitude of the magnetic field at <math> <0, 0, z> </math> at <math> \theta = 34 </math> degrees?<br />
<br />
Like before, we need to find <math> \vec r </math>, and then the magnitude. <math> \vec r = <0, 0, z> - < x, 0, 0> = <-x, 0, z> </math>. The magnitude is then <math> \sqrt{x^2 + z^2} </math>. <br />
We can then multiply the magnitudes of <math> q </math> and <math>\vec v </math> to get the final answer:<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{qvsin(34)}{(\sqrt{x^2 + z^2})^2} </math><br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
Right hand rule [[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]]<br />
Jean-Baptiste Biot [[http://www.physicsbook.gatech.edu/Jean-Baptiste_Biot]].<br />
<br />
===External links===<br />
<br />
"Teach Engineering" on Biot-Savart [https://www.teachengineering.org/view_lesson.php?url=collection/van_/lessons/van_mri_lesson_5/van_mri_lesson_5.xml]<br />
Derivation and Examples [http://study.com/academy/lesson/the-biot-savart-law-derivation-examples.html]<br />
Biot-Savart and Ampere's Law on MIT OpenCourse [http://ocw.mit.edu/high-school/physics/exam-prep/magnetic-fields/biot-savarts-law-amperes-law/]<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=16844Biot-Savart Law2015-12-05T23:41:48Z<p>Aboyd33: /* See also */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
An electron is located at the origin and moving at <math> 2e8 </math> m/s in the +x direction. What is the magnetic field at <math> <200, -300, 0> </math> m?<br />
<br />
First, we need to find <math> \vec r </math>, which in this case is just <math> \vec r = <200, -300, 0> </math> m. From that, we can calculate <math> \hat r </math>:<br />
<math> \hat r = \frac{ <200, -300, 0> }{\sqrt {200^2 + -300^2}}= <0.554, -0.832, 0> </math><br />
<br />
Next, we need to calculate <math> q \vec v </math>. Since we're dealing with an electron, our charge will be negative: <math> -1.6e-19* <2e8, 0, 0> = <-3.2e-11, 0, 0> </math>.<br />
Now for the cross product, <math> q\vec v\times\hat r </math>. The cross product is given as <math> \vec A\times\vec B = < AxBz - AzBy, AzBx - AxBz, AxBy-AyBz> </math>, so by using that formula we get <math> <0, 0, 2.65e-11> </math>. <br />
<br />
Finally, we can divide by the magnitude of <math> \vec r </math> squared: <math> \frac{ <0, 0, 2.65e-11> }{360.55} = <0, 0, 7.34e-14> </math>. Multiply by the constants and our final answer is <math> \vec B = <0, 0, 7.34e-21> Teslas </math><br />
<br />
===Example 2===<br />
A proton is located on the +x axis and is moving at a speed <math> \vec v </math> in the -y direction. What is the magnitude of the magnetic field at <math> <0, 0, z> </math> at <math> \theta = 34 </math> degrees?<br />
<br />
Like before, we need to find <math> \vec r </math>, and then the magnitude. <math> \vec r = <0, 0, z> - < x, 0, 0> = <-x, 0, z> </math>. The magnitude is then <math> \sqrt{x^2 + z^2} </math>. <br />
We can then multiply the magnitudes of <math> q </math> and <math>\vec v </math> to get the final answer:<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{qvsin(34)}{(\sqrt{x^2 + z^2})^2} </math><br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
Right hand rule [[http://www.physicsbook.gatech.edu/Right-Hand_Rule]]<br />
Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]]<br />
Jean-Baptiste Biot [[http://www.physicsbook.gatech.edu/Jean-Baptiste_Biot]].<br />
<br />
===External links===<br />
<br />
"Teach Engineering" on Biot-Savart [https://www.teachengineering.org/view_lesson.php?url=collection/van_/lessons/van_mri_lesson_5/van_mri_lesson_5.xml]<br />
Derivation and Examples [http://study.com/academy/lesson/the-biot-savart-law-derivation-examples.html]<br />
Biot-Savart and Ampere's Law on MIT OpenCourse [http://ocw.mit.edu/high-school/physics/exam-prep/magnetic-fields/biot-savarts-law-amperes-law/]<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=16774Biot-Savart Law2015-12-05T23:34:36Z<p>Aboyd33: /* See also */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
An electron is located at the origin and moving at <math> 2e8 </math> m/s in the +x direction. What is the magnetic field at <math> <200, -300, 0> </math> m?<br />
<br />
First, we need to find <math> \vec r </math>, which in this case is just <math> \vec r = <200, -300, 0> </math> m. From that, we can calculate <math> \hat r </math>:<br />
<math> \hat r = \frac{ <200, -300, 0> }{\sqrt {200^2 + -300^2}}= <0.554, -0.832, 0> </math><br />
<br />
Next, we need to calculate <math> q \vec v </math>. Since we're dealing with an electron, our charge will be negative: <math> -1.6e-19* <2e8, 0, 0> = <-3.2e-11, 0, 0> </math>.<br />
Now for the cross product, <math> q\vec v\times\hat r </math>. The cross product is given as <math> \vec A\times\vec B = < AxBz - AzBy, AzBx - AxBz, AxBy-AyBz> </math>, so by using that formula we get <math> <0, 0, 2.65e-11> </math>. <br />
<br />
Finally, we can divide by the magnitude of <math> \vec r </math> squared: <math> \frac{ <0, 0, 2.65e-11> }{360.55} = <0, 0, 7.34e-14> </math>. Multiply by the constants and our final answer is <math> \vec B = <0, 0, 7.34e-21> Teslas </math><br />
<br />
===Example 2===<br />
A proton is located on the +x axis and is moving at a speed <math> \vec v </math> in the -y direction. What is the magnitude of the magnetic field at <math> <0, 0, z> </math> at <math> \theta = 34 </math> degrees?<br />
<br />
Like before, we need to find <math> \vec r </math>, and then the magnitude. <math> \vec r = <0, 0, z> - < x, 0, 0> = <-x, 0, z> </math>. The magnitude is then <math> \sqrt{x^2 + z^2} </math>. <br />
We can then multiply the magnitudes of <math> q </math> and <math>\vec v </math> to get the final answer:<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{qvsin(34)}{(\sqrt{x^2 + z^2})^2} </math><br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
Right hand rule [[http://www.physicsbook.gatech.edu/Right-Hand_Rule]], <br />
<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=16763Biot-Savart Law2015-12-05T23:32:53Z<p>Aboyd33: /* Example 2 */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
An electron is located at the origin and moving at <math> 2e8 </math> m/s in the +x direction. What is the magnetic field at <math> <200, -300, 0> </math> m?<br />
<br />
First, we need to find <math> \vec r </math>, which in this case is just <math> \vec r = <200, -300, 0> </math> m. From that, we can calculate <math> \hat r </math>:<br />
<math> \hat r = \frac{ <200, -300, 0> }{\sqrt {200^2 + -300^2}}= <0.554, -0.832, 0> </math><br />
<br />
Next, we need to calculate <math> q \vec v </math>. Since we're dealing with an electron, our charge will be negative: <math> -1.6e-19* <2e8, 0, 0> = <-3.2e-11, 0, 0> </math>.<br />
Now for the cross product, <math> q\vec v\times\hat r </math>. The cross product is given as <math> \vec A\times\vec B = < AxBz - AzBy, AzBx - AxBz, AxBy-AyBz> </math>, so by using that formula we get <math> <0, 0, 2.65e-11> </math>. <br />
<br />
Finally, we can divide by the magnitude of <math> \vec r </math> squared: <math> \frac{ <0, 0, 2.65e-11> }{360.55} = <0, 0, 7.34e-14> </math>. Multiply by the constants and our final answer is <math> \vec B = <0, 0, 7.34e-21> Teslas </math><br />
<br />
===Example 2===<br />
A proton is located on the +x axis and is moving at a speed <math> \vec v </math> in the -y direction. What is the magnitude of the magnetic field at <math> <0, 0, z> </math> at <math> \theta = 34 </math> degrees?<br />
<br />
Like before, we need to find <math> \vec r </math>, and then the magnitude. <math> \vec r = <0, 0, z> - < x, 0, 0> = <-x, 0, z> </math>. The magnitude is then <math> \sqrt{x^2 + z^2} </math>. <br />
We can then multiply the magnitudes of <math> q </math> and <math>\vec v </math> to get the final answer:<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{qvsin(34)}{(\sqrt{x^2 + z^2})^2} </math><br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=16756Biot-Savart Law2015-12-05T23:31:45Z<p>Aboyd33: /* Examples */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
An electron is located at the origin and moving at <math> 2e8 </math> m/s in the +x direction. What is the magnetic field at <math> <200, -300, 0> </math> m?<br />
<br />
First, we need to find <math> \vec r </math>, which in this case is just <math> \vec r = <200, -300, 0> </math> m. From that, we can calculate <math> \hat r </math>:<br />
<math> \hat r = \frac{ <200, -300, 0> }{\sqrt {200^2 + -300^2}}= <0.554, -0.832, 0> </math><br />
<br />
Next, we need to calculate <math> q \vec v </math>. Since we're dealing with an electron, our charge will be negative: <math> -1.6e-19* <2e8, 0, 0> = <-3.2e-11, 0, 0> </math>.<br />
Now for the cross product, <math> q\vec v\times\hat r </math>. The cross product is given as <math> \vec A\times\vec B = < AxBz - AzBy, AzBx - AxBz, AxBy-AyBz> </math>, so by using that formula we get <math> <0, 0, 2.65e-11> </math>. <br />
<br />
Finally, we can divide by the magnitude of <math> \vec r </math> squared: <math> \frac{ <0, 0, 2.65e-11> }{360.55} = <0, 0, 7.34e-14> </math>. Multiply by the constants and our final answer is <math> \vec B = <0, 0, 7.34e-21> Teslas </math><br />
<br />
===Example 2===<br />
A proton is located on the +x axis and is moving at a speed <math> \vec v </math> in the -y direction. What is the magnitude of the magnetic field at <math> <0, 0, z> </math> at <math> \theta = 34 </math> degrees?<br />
<br />
Like before, we need to find <math> \vec r </math>, and then the magnitude. <math> \vec r = <0, 0, z> - < x, 0, 0> = <-x, 0, z> </math>. The magnitude is then <math> \sqrt{x^2 + z^2} </math>. <br />
We can then multiply the magnitudes of <math> q </math> and </math>\vec v </math> to get the final answer:<br />
<br />
<math> B = \frac{\mu_0}{4\pi}\frac{qv}{(\sqrt{x^2 + z^2})^2} </math><br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=16726Biot-Savart Law2015-12-05T23:29:17Z<p>Aboyd33: /* Example 2 */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
An electron is located at the origin and moving at <math> 2e8 </math> m/s in the +x direction. What is the magnetic field at <math> <200, -300, 0> </math> m?<br />
<br />
First, we need to find <math> \vec r </math>, which in this case is just <math> \vec r = <200, -300, 0> </math> m. From that, we can calculate <math> \hat r </math>:<br />
<math> \hat r = \frac{ <200, -300, 0> }{\sqrt {200^2 + -300^2}}= <0.554, -0.832, 0> </math><br />
<br />
Next, we need to calculate <math> q \vec v </math>. Since we're dealing with an electron, our charge will be negative: <math> -1.6e-19* <2e8, 0, 0> = <-3.2e-11, 0, 0> </math>.<br />
Now for the cross product, <math> q\vec v\times\hat r </math>. The cross product is given as <math> \vec A\times\vec B = < AxBz - AzBy, AzBx - AxBz, AxBy-AyBz> </math>, so by using that formula we get <math> <0, 0, 2.65e-11> </math>. <br />
<br />
Finally, we can divide by the magnitude of <math> \vec r </math> squared: <math> \frac{ <0, 0, 2.65e-11> }{360.55} = <0, 0, 7.34e-14> </math>. Multiply by the constants and our final answer is <math> \vec B = <0, 0, 7.34e-21> Teslas </math><br />
<br />
===Example 2===<br />
A proton is located on the +x axis and is moving at a speed <math> \vec v </math> in the -y direction. What is the magnitude of the magnetic field at <math> <0, 0, z> </math> at <math> \theta = 34 </math> degrees?<br />
<br />
Like before, we need to find <math> \vec r </math>, and then the magnitude. <math> \vec r = <0, 0, z> - < x, 0, 0> = <-x, 0, z> </math>. The magnitude is then <math> \sqrt{x^2 + z^2} </math>. <br />
We can then multiply the magnitudes of <math> q </math> and </math>\vec v </math> to get the final answer:<br />
<br />
<math> B =<br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=16547Biot-Savart Law2015-12-05T23:10:02Z<p>Aboyd33: /* Example 1 */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
An electron is located at the origin and moving at <math> 2e8 </math> m/s in the +x direction. What is the magnetic field at <math> <200, -300, 0> </math> m?<br />
<br />
First, we need to find <math> \vec r </math>, which in this case is just <math> \vec r = <200, -300, 0> </math> m. From that, we can calculate <math> \hat r </math>:<br />
<math> \hat r = \frac{ <200, -300, 0> }{\sqrt {200^2 + -300^2}}= <0.554, -0.832, 0> </math><br />
<br />
Next, we need to calculate <math> q \vec v </math>. Since we're dealing with an electron, our charge will be negative: <math> -1.6e-19* <2e8, 0, 0> = <-3.2e-11, 0, 0> </math>.<br />
Now for the cross product, <math> q\vec v\times\hat r </math>. The cross product is given as <math> \vec A\times\vec B = < AxBz - AzBy, AzBx - AxBz, AxBy-AyBz> </math>, so by using that formula we get <math> <0, 0, 2.65e-11> </math>. <br />
<br />
Finally, we can divide by the magnitude of <math> \vec r </math> squared: <math> \frac{ <0, 0, 2.65e-11> }{360.55} = <0, 0, 7.34e-14> </math>. Multiply by the constants and our final answer is <math> \vec B = <0, 0, 7.34e-21> Teslas </math><br />
<br />
===Example 2===<br />
A proton is located on the +x axis and is moving at a speed <math> \vec v </math> in the -y direction. What is the magnetic field at <math> \theta = 34 </math> degrees?<br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=16516Biot-Savart Law2015-12-05T23:05:01Z<p>Aboyd33: /* Example 1 */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
An electron is located at the origin and moving at <math> 2e8 </math> m/s in the +x direction. What is the magnetic field at <math> <200, -300, 0> </math> m?<br />
<br />
First, we need to find <math> \vec r </math>, which in this case is just <math> \vec r = <200, -300, 0> </math> m. From that, we can calculate <math> \hat r </math>:<br />
<math> \hat r = \frac{ <200, -300, 0> }{\sqrt {200^2 + -300^2}}= <0.554, -0.832, 0> </math><br />
<br />
Next, we need to calculate <math> q \vec v </math>. Since we're dealing with an electron, our charge will be negative: <math> -1.6e-19* <2e8, 0, 0> = <-3.2e-11, 0, 0> </math>.<br />
Now for the cross product, <math> q\vec v\times\hat r </math>. The cross product is given as <math> \vec A\times\vec B = <AxBz - AzBy, AzBx - AxBz, AxBy-AyBz> </math>, so by using that formula we get <math> <0, 0, 2.65e-11> </math>. <br />
<br />
Finally, we can divide by the magnitude of <math> \vec r </math> squared: <math> \frac{ <0, 0, 2.65e-11> }{360.55} = <0, 0, 7.34e-14> </math>. Multiply by the constants and our final answer is <math> \vec B = <0, 0, 7.34e-21> </math><br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=16456Biot-Savart Law2015-12-05T22:58:47Z<p>Aboyd33: /* Examples */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
An electron is located at the origin and moving at <math> 2e8 </math> m/s in the +x direction. What is the magnetic field at <math> <200, -300, 0> </math> m?<br />
<br />
First, we need to find <math> \vec r </math>, which in this case is just <math> \vec r = <200, -300, 0> </math> m. From that, we can calculate <math> \hat r </math>:<br />
<math> \hat r = \frac{ <200, -300, 0> }{\sqrt {200^2 + -300^2}}= <0.554, -0.832, 0> </math><br />
<br />
Next, we need to calculate <math> q \vec v </math>. Since we're dealing with an electron, our charge will be negative: <math> -1.6e-19* <2e8, 0, 0> = <-3.2e-11, 0, 0> </math>.<br />
Now for the cross product, <math> q \vec v x \hat r </math><br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=16422Biot-Savart Law2015-12-05T22:55:09Z<p>Aboyd33: /* Examples */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
An electron is located at the origin and moving at <math> 2e8 </math> m/s in the +x direction. What is the magnetic field at <math> <200, -300, 0> </math> m?<br />
<br />
First, we need to find <math> \vec r </math>, which in this case is just <math> \vec r = <200, -300, 0> </math> m. From that, we can calculate <math> \hat r </math>:<br />
<math> \hat r = \frac{ <200, -300, 0> }{\sqrt {200^2 + -300^2}}= <0.554, -0.832, 0> </math><br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=15374Biot-Savart Law2015-12-05T20:46:06Z<p>Aboyd33: /* See also */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
A point charge, <math> \vec q </math> is observed at +x direction with a velocity <math> \vec v </math> in the -y direction . If the source location is <math> <-x, -y, 0> </math>, what is the magnitude of the magnetic field generated due to the point charge?<br />
<br />
#The approach: In order to find the magnetic field at this point, we need to first find <math> \vec r </math>. Remember that <math> \vec r= \vec r(obs)- \vec r(source) </math><br />
<math> \vec r = <x, 0, 0>- <-x, -y, 0> = <2x, y, 0> </math><br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=15373Biot-Savart Law2015-12-05T20:45:32Z<p>Aboyd33: /* Examples */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
A point charge, <math> \vec q </math> is observed at +x direction with a velocity <math> \vec v </math> in the -y direction . If the source location is <math> <-x, -y, 0> </math>, what is the magnitude of the magnetic field generated due to the point charge?<br />
<br />
#The approach: In order to find the magnetic field at this point, we need to first find <math> \vec r </math>. Remember that <math> \vec r= \vec r(obs)- \vec r(source) </math><br />
<math> \vec r = <x, 0, 0>- <-x, -y, 0> = <2x, y, 0> </math><br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=15360Biot-Savart Law2015-12-05T20:43:31Z<p>Aboyd33: /* Examples */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
A point charge, <math> \vec q </math> is observed at +x direction with a velocity <math> \vec v </math> in the -y direction . If the source location is <math> <-x, -y, 0> </math>, what is the magnitude of the magnetic field generated due to the point charge?<br />
<br />
#The approach: In order to find the magnetic field at this point, we need to first find <math> \vec r </math>. Remember that <math> \vec r= \vec r(obs)- \vec r(source) </math><br />
\: <math> \vec r = <x, 0, 0>- <-x, -y, 0> = <2x, y, 0> </math><br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=15225Biot-Savart Law2015-12-05T20:24:50Z<p>Aboyd33: /* Examples */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
A point charge, <math> \vec q </math> is moving in the +z direction with a velocity <math> \vec v </math> in the -y direction . At a point in time, the point charge's location is <math> <x, y, 0> </math>. If the source location is <math> <0, -y, z> </math>, what is the magnetic field generated at that point?<br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=15148Biot-Savart Law2015-12-05T20:15:19Z<p>Aboyd33: /* A Computational Model */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[http://www.physicsbook.gatech.edu/Biot-Savart_Law_for_Currents]].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=15141Biot-Savart Law2015-12-05T20:14:19Z<p>Aboyd33: /* A Computational Model */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
For a computational model of a wire carrying current, see the wiki page on the Biot-Savart Law for Currents [[Link title]].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=15123Biot-Savart Law2015-12-05T20:12:55Z<p>Aboyd33: /* Applications */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
===Medical Technology===<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=15120Biot-Savart Law2015-12-05T20:12:23Z<p>Aboyd33: /* Medical Technology */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=File:Vortex.jpg&diff=15093File:Vortex.jpg2015-12-05T20:09:13Z<p>Aboyd33: Aboyd33 uploaded a new version of &quot;File:Vortex.jpg&quot;</p>
<hr />
<div></div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=15079Biot-Savart Law2015-12-05T20:07:04Z<p>Aboyd33: /* Applications */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
<br />
==Medical Technology==<br />
Aside from applications in aerospace engineering and chemistry, the Biot-Savart law also plays an important role in MRI imaging techniques. It's important to understand how a looped wire can create a current so these technologies can be as accurate as possible without harming patients who receive them.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=15025Biot-Savart Law2015-12-05T19:58:45Z<p>Aboyd33: /* History */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice in Metz in 1817, but gradually became more interested in physics than patients, particularly in sound and acoustics. He began building violins as a way to explore the form of the instrument through mathematical principles. <br />
<br />
In 1819, Savart officially closed the doors of his medical practice and went to Paris to find a publisher for the translation of ''De medicina''. While there, he attended a lecture on acoustics at by Jean-Baptiste Biot at the Faculty of Sciences. The two met there and began collaboration, when in 1820, Hans Christian Oersted published that a compass needle placed near a wire carrying current pointed at right angles to the wire. Biot and Savart began looking more closely into the field produced by a wire, and by using the oscillation of a magnetic dipole to determine the strength of the field close to a wire carrying current, they discovered what is now called the Biot-Savart Law [[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Savart.html]].<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=8372Biot-Savart Law2015-12-02T20:56:44Z<p>Aboyd33: /* History */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
<br />
==History==<br />
<br />
Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book ''De medicinia''. Savart began working on a translation and set up a medical practice, but gradually became more interested in physics than patients.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=8326Biot-Savart Law2015-12-02T20:42:33Z<p>Aboyd33: /* Aerodynamics */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:Vortex.jpg]]<br />
<br />
In this example,[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
<br />
==History==<br />
<br />
In 1820 two Frenchman, Felix Savart and Jean-Baptiste Biot, published ''Note sur le magnétisme de la pile de Volta'' and presented it to the Academy of Sciences in what became known as the Biot-Savart Law. Savart had been trained as a medical doctor, but began focusing more on physics rather than patients. He became interested in acoustics, building his own violins and conducting research on sound, and attended a lecture in Paris given by French mathematician, Jean-Baptiste Biot.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=File:Vortex.jpg&diff=8322File:Vortex.jpg2015-12-02T20:40:51Z<p>Aboyd33: </p>
<hr />
<div></div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=8309Biot-Savart Law2015-12-02T20:38:06Z<p>Aboyd33: /* Aerodynamics */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:vortex.jpg]]<br />
<br />
In this example[http://www.science20.com/news_articles/tendex_and_vortex_lines_new_way_visualize_warped_space_and_time-78171], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.<br />
<br />
==History==<br />
<br />
In 1820 two Frenchman, Felix Savart and Jean-Baptiste Biot, published ''Note sur le magnétisme de la pile de Volta'' and presented it to the Academy of Sciences in what became known as the Biot-Savart Law. Savart had been trained as a medical doctor, but began focusing more on physics rather than patients. He became interested in acoustics, building his own violins and conducting research on sound, and attended a lecture in Paris given by French mathematician, Jean-Baptiste Biot.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=8304Biot-Savart Law2015-12-02T20:34:27Z<p>Aboyd33: /* Aerodynamics */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.<br />
[[File:vortex.jpg]]<br />
<br />
==History==<br />
<br />
In 1820 two Frenchman, Felix Savart and Jean-Baptiste Biot, published ''Note sur le magnétisme de la pile de Volta'' and presented it to the Academy of Sciences in what became known as the Biot-Savart Law. Savart had been trained as a medical doctor, but began focusing more on physics rather than patients. He became interested in acoustics, building his own violins and conducting research on sound, and attended a lecture in Paris given by French mathematician, Jean-Baptiste Biot.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=8277Biot-Savart Law2015-12-02T20:22:39Z<p>Aboyd33: </p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Applications==<br />
===Magnetic Response===<br />
The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance]<br />
===Aerodynamics===<br />
<br />
==History==<br />
<br />
In 1820 two Frenchman, Felix Savart and Jean-Baptiste Biot, published ''Note sur le magnétisme de la pile de Volta'' and presented it to the Academy of Sciences in what became known as the Biot-Savart Law. Savart had been trained as a medical doctor, but began focusing more on physics rather than patients. He became interested in acoustics, building his own violins and conducting research on sound, and attended a lecture in Paris given by French mathematician, Jean-Baptiste Biot.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=5987Biot-Savart Law2015-12-01T17:46:51Z<p>Aboyd33: /* Connectedness */</p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Applications==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
In 1820 two Frenchman, Felix Savart and Jean-Baptiste Biot, published ''Note sur le magnétisme de la pile de Volta'' and presented it to the Academy of Sciences in what became known as the Biot-Savart Law. Savart had been trained as a medical doctor, but began focusing more on physics rather than patients. He became interested in acoustics, building his own violins and conducting research on sound, and attended a lecture in Paris given by French mathematician, Jean-Baptiste Biot.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=4564Biot-Savart Law2015-11-30T19:06:32Z<p>Aboyd33: </p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation location (remember <math> r= r(obs)-r(source) </math>)<br />
<br />
Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: <math> B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
In 1820 two Frenchman, Felix Savart and Jean-Baptiste Biot, published ''Note sur le magnétisme de la pile de Volta'' and presented it to the Academy of Sciences in what became known as the Biot-Savart Law. Savart had been trained as a medical doctor, but began focusing more on physics rather than patients. He became interested in acoustics, building his own violins and conducting research on sound, and attended a lecture in Paris given by French mathematician, Jean-Baptiste Biot.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33http://www.physicsbook.gatech.edu/index.php?title=Biot-Savart_Law&diff=4556Biot-Savart Law2015-11-30T18:53:42Z<p>Aboyd33: </p>
<hr />
<div>The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]<br />
<br />
==The Main Idea==<br />
<br />
An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.<br />
<br />
===A Mathematical Model===<br />
<br />
The general formula for a single charge is <math>\vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} </math> where <math> \mu_0 </math> is the constant <math> 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} </math> exactly. <math> \vec q </math> is the velocity of the point charge <math> q </math> and <math> \hat r </math> is the unit vector pointing from the source towards the observation (remember <math> r= r(obs)-r(source) <\math>)<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
In 1820 two Frenchman, Felix Savart and Jean-Baptiste Biot, published ''Note sur le magnétisme de la pile de Volta'' and presented it to the Academy of Sciences in what became known as the Biot-Savart Law. Savart had been trained as a medical doctor, but began focusing more on physics rather than patients. He became interested in acoustics, building his own violins and conducting research on sound, and attended a lecture in Paris given by French mathematician, Jean-Baptiste Biot.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Aboyd33