Physics Book - User contributions [en]

Magnetic Field

2016-04-18T01:26:50Z

Skim773:

Claimed by Seongshik Kim Spring 2016

This page discusses the general properties and characteristics of magnetic fields

== Magnetic Field==

Unlike electric fields, magnetic fields are made by moving charges. Stationary charges do not exert magnetic fields. In equilibrium, there is no net motion of charges inside a metal. Therefore, it should be noted that electrons inside a metal must move continuously. This is the very basic definition of the current, a non-equilibrium system in which there is a constant flow of electrons in order to create a magnetic field.

[[File:field111.JPG]]

There are a few important main concepts to understand before proceeding further. First, the direction of the magnetic field is perpendicular to the direction of the current. Second, equilibrium and being continuous are totally different things.

===A Mathematical Model===
The magnetic field created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savart law. You may notice that this equation involves a cross product.

== characteristics of the Biot-Savart Law==
[[File:Field3.JPG]]

Because the equation involves the cross product of velocity and the position vector, one can find out that there is no magnetic field in the direction of the movement of the charged particle, because the cross product of two vectors in the same direction is zero.

[[File:Field2.JPG]]

However, even in the absence of a magnetic field, an electric field may still be present.

By using a compass, one can calculate the magnitude of a current. The Earth exerts a magnitude that always points to the North. When a compass is near a current with a magnetic field, the needle would be deflected by the net magnetic field. Notice that although the magnetic field of the current is perpendicular to the direction of the movement of charges, the needle is not deflected 90 degrees because of the magnetic field of the Earth, which is usually larger than that of the current. Also, because the magnetic field is exerted in a circular pattern, the direction of the magnetic field above the source is exactly the opposite of the magnetic field under the source. As a result, depending on the location of the compass, the needle may deflect in the opposite direction but with the same magnitude.

[[File:field4.JPG]]

Lastly, Because of the direction of the magnetic field is influenced by the charge of the source, charge, in this case, one must pay attention to the presence of Q in the equation above.

[[File:field6.JPG]]

==Connectedness==
This is the foundation of Physics II, for many of the materials one learns is based on the electric field and the magnetic field. Once one understand how magnetic fields are created and affected by charges, one will be able to apply the knowledge to find out what is going on in currents. For instance, in a metal positively charged particles are not likely to move compared to electrons due to their heavy weight. However, electrons, being negatively charged, hinder one's ability to calculate relevant applications. Thus, the concept of the conventional current is introduced to explain not only the general flow of current in a circuit, but also describe macroscopic behaviors, including resistance and capacitance, of circuits. Therefore, one must be able to distinguish key differences between the magnetic field and the electric field and how they are applied. In addition, the cross product is used, so one must be familiar with the right hand rule as well.

Page initiated by --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 14:20, 19 October 2015 (EDT)
edited by Seongshik Kim 21:20, 17 April 2016
[[Category: Fields]]

Magnetic Field

2016-04-18T01:26:23Z

Skim773:

Claimed by Seongshik Kim spring 2016

This page discusses the general properties and characteristics of magnetic fields

== Magnetic Field==

Unlike electric fields, magnetic fields are made by moving charges. Stationary charges do not exert magnetic fields. In equilibrium, there is no net motion of charges inside a metal. Therefore, it should be noted that electrons inside a metal must move continuously. This is the very basic definition of the current, a non-equilibrium system in which there is a constant flow of electrons in order to create a magnetic field.

[[File:field111.JPG]]

There are a few important main concepts to understand before proceeding further. First, the direction of the magnetic field is perpendicular to the direction of the current. Second, equilibrium and being continuous are totally different things.

===A Mathematical Model===
The magnetic field created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savart law. You may notice that this equation involves a cross product.

== characteristics of the Biot-Savart Law==
[[File:Field3.JPG]]

Because the equation involves the cross product of velocity and the position vector, one can find out that there is no magnetic field in the direction of the movement of the charged particle, because the cross product of two vectors in the same direction is zero.

[[File:Field2.JPG]]

However, even in the absence of a magnetic field, an electric field may still be present.

By using a compass, one can calculate the magnitude of a current. The Earth exerts a magnitude that always points to the North. When a compass is near a current with a magnetic field, the needle would be deflected by the net magnetic field. Notice that although the magnetic field of the current is perpendicular to the direction of the movement of charges, the needle is not deflected 90 degrees because of the magnetic field of the Earth, which is usually larger than that of the current. Also, because the magnetic field is exerted in a circular pattern, the direction of the magnetic field above the source is exactly the opposite of the magnetic field under the source. As a result, depending on the location of the compass, the needle may deflect in the opposite direction but with the same magnitude.

[[File:field4.JPG]]

Lastly, Because of the direction of the magnetic field is influenced by the charge of the source, charge, in this case, one must pay attention to the presence of Q in the equation above.

[[File:field6.JPG]]

==Connectedness==
This is the foundation of Physics II, for many of the materials one learns is based on the electric field and the magnetic field. Once one understand how magnetic fields are created and affected by charges, one will be able to apply the knowledge to find out what is going on in currents. For instance, in a metal positively charged particles are not likely to move compared to electrons due to their heavy weight. However, electrons, being negatively charged, hinder one's ability to calculate relevant applications. Thus, the concept of the conventional current is introduced to explain not only the general flow of current in a circuit, but also describe macroscopic behaviors, including resistance and capacitance, of circuits. Therefore, one must be able to distinguish key differences between the magnetic field and the electric field and how they are applied. In addition, the cross product is used, so one must be familiar with the right hand rule as well.

Page initiated by --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 14:20, 19 October 2015 (EDT)
edited by Seongshik Kim 21:20, 17 April 2016
[[Category: Fields]]

Magnetic Field

2016-04-18T01:20:22Z

Skim773:

Claimed by Seongshik Kim spring 2016

This page discusses the general properties and characteristics of magnetic fields

== Magnetic Field==

Unlike electric fields, magnetic fields are made by moving charges. Stationary charges do not exert magnetic fields. In equilibrium, there is no net motion of charges inside a metal. Therefore, it should be noted that electrons inside a metal must move continuously. This is the very basic definition of the current, a non-equilibrium system in which there is a constant flow of electrons in order to create a magnetic field.

[[File:field111.JPG]]

There are a few important main concepts to understand before proceeding further. First, the direction of the magnetic field is perpendicular to the direction of the current. Second, equilibrium and being continuous are totally different things.

===A Mathematical Model===
The magnetic field created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savart law. You may notice that this equation involves a cross product.

== characteristics of the Biot-Savart Law==
[[File:Field3.JPG]]

Because the equation involves the cross product of velocity and the position vector, one can find out that there is no magnetic field in the direction of the movement of the charged particle, because the cross product of two vectors in the same direction is zero.

[[File:Field2.JPG]]

However, even in the absence of a magnetic field, an electric field may still be present.

By using a compass, one can calculate the magnitude of a current. The Earth exerts a magnitude that always points to the North. When a compass is near a current with a magnetic field, the needle would be deflected by the net magnetic field. Notice that although the magnetic field of the current is perpendicular to the direction of the movement of charges, the needle is not deflected 90 degrees because of the magnetic field of the Earth, which is usually larger than that of the current. Also, because the magnetic field is exerted in a circular pattern, the direction of the magnetic field above the source is exactly the opposite of the magnetic field under the source. As a result, depending on the location of the compass, the needle may deflect in the opposite direction but with the same magnitude.

[[File:field4.JPG]]

Lastly, Because of the direction of the magnetic field is influenced by the charge of the source, charge, in this case, one must pay attention to the presence of Q in the equation above.

[[File:field6.JPG]]

Page initiated by --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 14:20, 19 October 2015 (EDT)
edited by Seongshik Kim 21:20, 17 April 2016
[[Category: Fields]]

Magnetic Field

2016-04-18T01:19:49Z

Skim773:

Claimed by Seongshik Kim spring 2016

This page discusses the general properties and characteristics of magnetic fields

== Magnetic Field==

Unlike electric fields, magnetic fields are made by moving charges. Stationary charges do not exert magnetic fields. In equilibrium, there is no net motion of charges inside a metal. Therefore, it should be noted that electrons inside a metal must move continuously. This is the very basic definition of the current, a non-equilibrium system in which there is a constant flow of electrons in order to create a magnetic field.

[[File:field111.JPG]]

There are a few important main concepts to understand before proceeding further. First, the direction of the magnetic field is perpendicular to the direction of the current. Second, equilibrium and being continuous are totally different things.

===A Mathematical Model===
The magnetic field created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savart law. You may notice that this equation involves a cross product.

== characteristics of the Biot-Savart Law==
[[File:Field3.JPG]]

Because the equation involves the cross product of velocity and the position vector, one can find out that there is no magnetic field in the direction of the movement of the charged particle, because the cross product of two vectors in the same direction is zero.

[[File:Field2.JPG]]

However, even in the absence of a magnetic field, an electric field may still be present.

By using a compass, one can calculate the magnitude of a current. The Earth exerts a magnitude that always points to the North. When a compass is near a current with a magnetic field, the needle would be deflected by the net magnetic field. Notice that although the magnetic field of the current is perpendicular to the direction of the movement of charges, the needle is not deflected 90 degrees because of the magnetic field of the Earth, which is usually larger than that of the current. Also, because the magnetic field is exerted in a circular pattern, the direction of the magnetic field above the source is exactly the opposite of the magnetic field under the source. As a result, depending on the location of the compass, the needle may deflect in the opposite direction but with the same magnitude.
[[File:field4.JPG]]

Lastly, Because of the direction of the magnetic field is influenced by the charge of the source, charge, in this case, one must pay attention to the presence of Q in the equation above.
[[File:field6.JPG]]

Page initiated by --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 14:20, 19 October 2015 (EDT)
edited by Seongshik Kim 21:20, 17 April 2016
[[Category: Fields]]

File:Field6.JPG

2016-04-18T01:19:02Z

Skim773:

File:Field5.jpg

2016-04-18T01:13:52Z

Skim773:

Magnetic Field

2016-04-18T01:12:36Z

Skim773:

Claimed by Seongshik Kim spring 2016

This page discusses the general properties and characteristics of magnetic fields

== Magnetic Field==

Unlike electric fields, magnetic fields are made by moving charges. Stationary charges do not exert magnetic fields. In equilibrium, there is no net motion of charges inside a metal. Therefore, it should be noted that electrons inside a metal must move continuously. This is the very basic definition of the current, a non-equilibrium system in which there is a constant flow of electrons in order to create a magnetic field.

[[File:field111.JPG]]

There are a few important main concepts to understand before proceeding further. First, the direction of the magnetic field is perpendicular to the direction of the current. Second, equilibrium and being continuous are totally different things.

===A Mathematical Model===
The magnetic field created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savart law. You may notice that this equation involves a cross product.

== characteristics of the Biot-Savart Law==
[[File:Field3.JPG]]

Because the equation involves the cross product of velocity and the position vector, one can find out that there is no magnetic field in the direction of the movement of the charged particle, because the cross product of two vectors in the same direction is zero.

[[File:Field2.JPG]]

However, even in the absence of a magnetic field, an electric field may still be present.

By using a compass, one can calculate the magnitude of a current. The Earth exerts a magnitude that always points to the North. When a compass is near a current with a magnetic field, the needle would be deflected by the net magnetic field. Notice that although the magnetic field of the current is perpendicular to the direction of the movement of charges, the needle is not deflected 90 degrees because of the magnetic field of the Earth, which is usually larger than that of the current. Also, because the magnetic field is exerted in a circular pattern, the direction of the magnetic field above the source is exactly the opposite of the magnetic field under the source. As a result, depending on the location of the compass, the needle may deflect in the opposite direction but with the same magnitude.
[[File:field4.JPG]]

Lastly, one must pay attention to the presence of <math> \q = 0</math>

== Dependence on frame of reference== (<math> \vec{v} = 0</math>)

== Magnetic field due to a single charged particle==

The magnetic field <math> \vec{B}</math> created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savarde law. You may notice that this equation involves a cross product.

Page initiated by --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 14:20, 19 October 2015 (EDT)
[[Category: Fields]]

Magnetic Field

2016-04-18T01:11:18Z

Skim773:

Claimed by Seongshik Kim spring 2016

This page discusses the general properties and characteristics of magnetic fields

== Magnetic Field==

Unlike electric fields, magnetic fields are made by moving charges. Stationary charges do not exert magnetic fields. In equilibrium, there is no net motion of charges inside a metal. Therefore, it should be noted that electrons inside a metal must move continuously. This is the very basic definition of the current, a non-equilibrium system in which there is a constant flow of electrons in order to create a magnetic field.

[[File:field111.JPG]]

There are a few important main concepts to understand before proceeding further. First, the direction of the magnetic field is perpendicular to the direction of the current. Second, equilibrium and being continuous are totally different things.

===A Mathematical Model===
The magnetic field created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savart law. You may notice that this equation involves a cross product.

== characteristics of the Biot-Savart Law==
[[File:Field3.JPG]]

Because the equation involves the cross product of velocity and the position vector, one can find out that there is no magnetic field in the direction of the movement of the charged particle, because the cross product of two vectors in the same direction is zero.

[[File:Field2.JPG]]

However, even in the absence of a magnetic field, an electric field may still be present.

By using a compass, one can calculate the magnitude of a current. The Earth exerts a magnitude that always points to the North. When a compass is near a current with a magnetic field, the needle would be deflected by the net magnetic field. Notice that although the magnetic field of the current is perpendicular to the direction of the movement of charges, the needle is not deflected 90 degrees because of the magnetic field of the Earth, which is usually larger than that of the current. Also, because the magnetic field is exerted in a circular pattern, the direction of the magnetic field above the source is exactly the opposite of the magnetic field under the source. As a result, depending on the location of the compass, the needle may deflect in the opposite direction but with the same magnitude.[[File:field4.JPG]]

== Dependence on frame of reference== (<math> \vec{v} = 0</math>)

== Magnetic field due to a single charged particle==

The magnetic field <math> \vec{B}</math> created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savarde law. You may notice that this equation involves a cross product.

Page initiated by --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 14:20, 19 October 2015 (EDT)
[[Category: Fields]]

Magnetic Field

2016-04-18T01:10:54Z

Skim773:

Claimed by Seongshik Kim spring 2016

This page discusses the general properties and characteristics of magnetic fields

== Magnetic Field==

Unlike electric fields, magnetic fields are made by moving charges. Stationary charges do not exert magnetic fields. In equilibrium, there is no net motion of charges inside a metal. Therefore, it should be noted that electrons inside a metal must move continuously. This is the very basic definition of the current, a non-equilibrium system in which there is a constant flow of electrons in order to create a magnetic field.

[[File:field111.JPG]]

There are a few important main concepts to understand before proceeding further. First, the direction of the magnetic field is perpendicular to the direction of the current. Second, equilibrium and being continuous are totally different things.

===A Mathematical Model===
The magnetic field created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savart law. You may notice that this equation involves a cross product.

== characteristics of the Biot-Savart Law==
[[File:Field3.JPG]]
Because the equation involves the cross product of velocity and the position vector, one can find out that there is no magnetic field in the direction of the movement of the charged particle, because the cross product of two vectors in the same direction is zero.

[[File:Field2.JPG]]
However, even in the absence of a magnetic field, an electric field may still be present.

By using a compass, one can calculate the magnitude of a current. The Earth exerts a magnitude that always points to the North. When a compass is near a current with a magnetic field, the needle would be deflected by the net magnetic field. Notice that although the magnetic field of the current is perpendicular to the direction of the movement of charges, the needle is not deflected 90 degrees because of the magnetic field of the Earth, which is usually larger than that of the current. [[File:field4.JPG]]Also, because the magnetic field is exerted in a circular pattern, the direction of the magnetic field above the source is exactly the opposite of the magnetic field under the source. As a result, depending on the location of the compass, the needle may deflect in the opposite direction but with the same magnitude.

== Dependence on frame of reference== (<math> \vec{v} = 0</math>)

== Magnetic field due to a single charged particle==

The magnetic field <math> \vec{B}</math> created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savarde law. You may notice that this equation involves a cross product.

Page initiated by --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 14:20, 19 October 2015 (EDT)
[[Category: Fields]]

Magnetic Field

2016-04-18T01:10:26Z

Skim773:

Claimed by Seongshik Kim spring 2016

This page discusses the general properties and characteristics of magnetic fields

== Magnetic Field==

Unlike electric fields, magnetic fields are made by moving charges. Stationary charges do not exert magnetic fields. In equilibrium, there is no net motion of charges inside a metal. Therefore, it should be noted that electrons inside a metal must move continuously. This is the very basic definition of the current, a non-equilibrium system in which there is a constant flow of electrons in order to create a magnetic field.

[[File:field111.JPG]]

There are a few important main concepts to understand before proceeding further. First, the direction of the magnetic field is perpendicular to the direction of the current. Second, equilibrium and being continuous are totally different things.

===A Mathematical Model===
The magnetic field created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savart law. You may notice that this equation involves a cross product.

== characteristics of the Biot-Savart Law==
Because the equation involves the cross product of velocity and the position vector, one can find out that there is no magnetic field in the direction of the movement of the charged particle, because the cross product of two vectors in the same direction is zero. [[File:Field3.JPG]]

[[File:Field2.JPG]]
However, even in the absence of a magnetic field, an electric field may still be present.

By using a compass, one can calculate the magnitude of a current. The Earth exerts a magnitude that always points to the North. When a compass is near a current with a magnetic field, the needle would be deflected by the net magnetic field. Notice that although the magnetic field of the current is perpendicular to the direction of the movement of charges, the needle is not deflected 90 degrees because of the magnetic field of the Earth, which is usually larger than that of the current. [[File:field4.JPG]]Also, because the magnetic field is exerted in a circular pattern, the direction of the magnetic field above the source is exactly the opposite of the magnetic field under the source. As a result, depending on the location of the compass, the needle may deflect in the opposite direction but with the same magnitude.

== Dependence on frame of reference== (<math> \vec{v} = 0</math>)

== Magnetic field due to a single charged particle==

The magnetic field <math> \vec{B}</math> created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savarde law. You may notice that this equation involves a cross product.

Page initiated by --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 14:20, 19 October 2015 (EDT)
[[Category: Fields]]

File:Field4.JPG

2016-04-18T01:10:12Z

Skim773:

Magnetic Field

2016-04-18T01:08:02Z

Skim773:

Claimed by Seongshik Kim spring 2016

This page discusses the general properties and characteristics of magnetic fields

== Magnetic Field==

Unlike electric fields, magnetic fields are made by moving charges. Stationary charges do not exert magnetic fields. In equilibrium, there is no net motion of charges inside a metal. Therefore, it should be noted that electrons inside a metal must move continuously. This is the very basic definition of the current, a non-equilibrium system in which there is a constant flow of electrons in order to create a magnetic field.

[[File:field111.JPG]]

There are a few important main concepts to understand before proceeding further. First, the direction of the magnetic field is perpendicular to the direction of the current. Second, equilibrium and being continuous are totally different things.

===A Mathematical Model===
The magnetic field created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savart law. You may notice that this equation involves a cross product.

== characteristics of the Biot-Savart Law==
Because the equation involves the cross product of velocity and the position vector, one can find out that there is no magnetic field in the direction of the movement of the charged particle, because the cross product of two vectors in the same direction is zero. [[File:Field3.JPG]]

However, even in the absence of a magnetic field, an electric field may still be present. [[File:Field2.JPG]]

By using a compass, one can calculate the magnitude of a current. The Earth exerts a magnitude that always points to the North. When a compass is near a current with a magnetic field, the needle would be deflected by the net magnetic field. Notice that although the magnetic field of the current is perpendicular to the direction of the movement of charges, the needle is not deflected 90 degrees because of the magnetic field of the Earth, which is usually larger than that of the current. Also, because the magnetic field is exerted in a circular pattern, the direction of the magnetic field above the source is exactly the opposite of the magnetic field under the source. As a result, depending on the location of the compass, the needle may deflect in the opposite direction but with the same magnitude.

== Dependence on frame of reference== (<math> \vec{v} = 0</math>)

== Magnetic field due to a single charged particle==

The magnetic field <math> \vec{B}</math> created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savarde law. You may notice that this equation involves a cross product.

Page initiated by --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 14:20, 19 October 2015 (EDT)
[[Category: Fields]]

File:Field3.JPG

2016-04-18T01:06:04Z

Skim773:

File:Field2.JPG

2016-04-18T01:05:47Z

Skim773:

Magnetic Field

2016-04-18T01:00:59Z

Skim773:

Claimed by Seongshik Kim spring 2016

This page discusses the general properties and characteristics of magnetic fields

== Magnetic Field==

Unlike electric fields, magnetic fields are made by moving charges. Stationary charges do not exert magnetic fields. In equilibrium, there is no net motion of charges inside a metal. Therefore, it should be noted that electrons inside a metal must move continuously. This is the very basic definition of the current, a non-equilibrium system in which there is a constant flow of electrons in order to create a magnetic field.

[[File:field111.JPG]]

There are a few important main concepts to understand before proceeding further. First, the direction of the magnetic field is perpendicular to the direction of the current. Second, equilibrium and being continuous are totally different things.

===A Mathematical Model===
The magnetic field created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savart law. You may notice that this equation involves a cross product.

== characteristics of the Biot-Savart Law==
Because the equation involves the cross product of velocity and the position vector, one can find out that there is no magnetic field in the direction of the movement of the charged particle, because the cross product of two vectors in the same direction is zero.

However, even in the absence of a magnetic field, an electric field may still be present.

By using a compass, one can calculate the magnitude of a current. The Earth exerts a magnitude that always points to the North. When a compass is near a current with a magnetic field, the needle would be deflected by the net magnetic field. Notice that although the magnetic field of the current is perpendicular to the direction of the movement of charges, the needle is not deflected 90 degrees because of the magnetic field of the Earth, which is usually larger than that of the current. Also, because the magnetic field is exerted in a circular pattern, the direction of the magnetic field above the source is exactly the opposite of the magnetic field under the source. As a result, depending on the location of the compass, the needle may deflect in the opposite direction but with the same magnitude.

== Dependence on frame of reference== (<math> \vec{v} = 0</math>)

== Magnetic field due to a single charged particle==

The magnetic field <math> \vec{B}</math> created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savarde law. You may notice that this equation involves a cross product.

Page initiated by --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 14:20, 19 October 2015 (EDT)
[[Category: Fields]]

File:Field111.JPG

2016-04-18T01:00:46Z

Skim773:

Magnetic Field

2016-04-18T01:00:03Z

Skim773:

Claimed by Seongshik Kim spring 2016

This page discusses the general properties and characteristics of magnetic fields

== Magnetic Field==

Unlike electric fields, magnetic fields are made by moving charges. Stationary charges do not exert magnetic fields. In equilibrium, there is no net motion of charges inside a metal. Therefore, it should be noted that electrons inside a metal must move continuously. This is the very basic definition of the current, a non-equilibrium system in which there is a constant flow of electrons in order to create a magnetic field.

[[File:field11.JPG]]

There are a few important main concepts to understand before proceeding further. First, the direction of the magnetic field is perpendicular to the direction of the current. Second, equilibrium and being continuous are totally different things.

===A Mathematical Model===
The magnetic field created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savart law. You may notice that this equation involves a cross product.

== characteristics of the Biot-Savart Law==
Because the equation involves the cross product of velocity and the position vector, one can find out that there is no magnetic field in the direction of the movement of the charged particle, because the cross product of two vectors in the same direction is zero.

However, even in the absence of a magnetic field, an electric field may still be present.

By using a compass, one can calculate the magnitude of a current. The Earth exerts a magnitude that always points to the North. When a compass is near a current with a magnetic field, the needle would be deflected by the net magnetic field. Notice that although the magnetic field of the current is perpendicular to the direction of the movement of charges, the needle is not deflected 90 degrees because of the magnetic field of the Earth, which is usually larger than that of the current. Also, because the magnetic field is exerted in a circular pattern, the direction of the magnetic field above the source is exactly the opposite of the magnetic field under the source. As a result, depending on the location of the compass, the needle may deflect in the opposite direction but with the same magnitude.

== Dependence on frame of reference== (<math> \vec{v} = 0</math>)

== Magnetic field due to a single charged particle==

The magnetic field <math> \vec{B}</math> created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savarde law. You may notice that this equation involves a cross product.

Page initiated by --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 14:20, 19 October 2015 (EDT)
[[Category: Fields]]

Magnetic Field

2016-04-18T00:59:48Z

Skim773:

Claimed by Seongshik Kim spring 2016

This page discusses the general properties and characteristics of magnetic fields

== Magnetic Field==

Unlike electric fields, magnetic fields are made by moving charges. Stationary charges do not exert magnetic fields. In equilibrium, there is no net motion of charges inside a metal. Therefore, it should be noted that electrons inside a metal must move continuously. This is the very basic definition of the current, a non-equilibrium system in which there is a constant flow of electrons in order to create a magnetic field.

[[File:field11.jpg]]

There are a few important main concepts to understand before proceeding further. First, the direction of the magnetic field is perpendicular to the direction of the current. Second, equilibrium and being continuous are totally different things.

===A Mathematical Model===
The magnetic field created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savart law. You may notice that this equation involves a cross product.

== characteristics of the Biot-Savart Law==
Because the equation involves the cross product of velocity and the position vector, one can find out that there is no magnetic field in the direction of the movement of the charged particle, because the cross product of two vectors in the same direction is zero.

However, even in the absence of a magnetic field, an electric field may still be present.

By using a compass, one can calculate the magnitude of a current. The Earth exerts a magnitude that always points to the North. When a compass is near a current with a magnetic field, the needle would be deflected by the net magnetic field. Notice that although the magnetic field of the current is perpendicular to the direction of the movement of charges, the needle is not deflected 90 degrees because of the magnetic field of the Earth, which is usually larger than that of the current. Also, because the magnetic field is exerted in a circular pattern, the direction of the magnetic field above the source is exactly the opposite of the magnetic field under the source. As a result, depending on the location of the compass, the needle may deflect in the opposite direction but with the same magnitude.

== Dependence on frame of reference== (<math> \vec{v} = 0</math>)

== Magnetic field due to a single charged particle==

The magnetic field <math> \vec{B}</math> created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savarde law. You may notice that this equation involves a cross product.

Page initiated by --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 14:20, 19 October 2015 (EDT)
[[Category: Fields]]

File:Field11.JPG

2016-04-18T00:59:26Z

Skim773:

Magnetic Field

2016-04-18T00:56:26Z

Skim773:

Claimed by Seongshik Kim spring 2016

This page discusses the general properties and characteristics of magnetic fields

== Magnetic Field==

[[File:Example.jpg]]

Unlike electric fields, magnetic fields are made by moving charges. Stationary charges do not exert magnetic fields. In equilibrium, there is no net motion of charges inside a metal. Therefore, it should be noted that electrons inside a metal must move continuously. This is the very basic definition of the current, a non-equilibrium system in which there is a constant flow of electrons in order to create a magnetic field.

[[File:field1.jpg]]

There are a few important main concepts to understand before proceeding further. First, the direction of the magnetic field is perpendicular to the direction of the current. Second, equilibrium and being continuous are totally different things.

===A Mathematical Model===
The magnetic field created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savart law. You may notice that this equation involves a cross product.

== characteristics of the Biot-Savart Law==
Because the equation involves the cross product of velocity and the position vector, one can find out that there is no magnetic field in the direction of the movement of the charged particle, because the cross product of two vectors in the same direction is zero.

However, even in the absence of a magnetic field, an electric field may still be present.

By using a compass, one can calculate the magnitude of a current. The Earth exerts a magnitude that always points to the North. When a compass is near a current with a magnetic field, the needle would be deflected by the net magnetic field. Notice that although the magnetic field of the current is perpendicular to the direction of the movement of charges, the needle is not deflected 90 degrees because of the magnetic field of the Earth, which is usually larger than that of the current. Also, because the magnetic field is exerted in a circular pattern, the direction of the magnetic field above the source is exactly the opposite of the magnetic field under the source. As a result, depending on the location of the compass, the needle may deflect in the opposite direction but with the same magnitude.

== Dependence on frame of reference== (<math> \vec{v} = 0</math>)

== Magnetic field due to a single charged particle==

The magnetic field <math> \vec{B}</math> created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savarde law. You may notice that this equation involves a cross product.

Page initiated by --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 14:20, 19 October 2015 (EDT)
[[Category: Fields]]

File:Field1.jpg

2016-04-18T00:51:48Z

Skim773:

Magnetic Field

2016-04-18T00:50:32Z

Skim773:

Claimed by Seongshik Kim spring 2016

This page discusses the general properties and characteristics of magnetic fields

== Magnetic Field==

Unlike electric fields, magnetic fields are made by moving charges. Stationary charges do not exert magnetic fields. In equilibrium, there is no net motion of charges inside a metal. Therefore, it should be noted that electrons inside a metal must move continuously. This is the very basic definition of the current, a non-equilibrium system in which there is a constant flow of electrons in order to create a magnetic field.

[[File:field1.jpg]]

There are a few important main concepts to understand before proceeding further. First, the direction of the magnetic field is perpendicular to the direction of the current. Second, equilibrium and being continuous are totally different things.

===A Mathematical Model===
The magnetic field created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savart law. You may notice that this equation involves a cross product.

== characteristics of the Biot-Savart Law==
Because the equation involves the cross product of velocity and the position vector, one can find out that there is no magnetic field in the direction of the movement of the charged particle, because the cross product of two vectors in the same direction is zero.

However, even in the absence of a magnetic field, an electric field may still be present.

By using a compass, one can calculate the magnitude of a current. The Earth exerts a magnitude that always points to the North. When a compass is near a current with a magnetic field, the needle would be deflected by the net magnetic field. Notice that although the magnetic field of the current is perpendicular to the direction of the movement of charges, the needle is not deflected 90 degrees because of the magnetic field of the Earth, which is usually larger than that of the current. Also, because the magnetic field is exerted in a circular pattern, the direction of the magnetic field above the source is exactly the opposite of the magnetic field under the source. As a result, depending on the location of the compass, the needle may deflect in the opposite direction but with the same magnitude.

== Dependence on frame of reference== (<math> \vec{v} = 0</math>)

== Magnetic field due to a single charged particle==

The magnetic field <math> \vec{B}</math> created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savarde law. You may notice that this equation involves a cross product.

Page initiated by --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 14:20, 19 October 2015 (EDT)
[[Category: Fields]]

Magnetic Field

2016-04-18T00:46:24Z

Skim773:

Claimed by Seongshik Kim spring 2016

This page discusses the general properties and characteristics of magnetic fields

== Magnetic Field==

Unlike electric fields, magnetic fields are made by moving charges. Stationary charges do not exert magnetic fields. In equilibrium, there is no net motion of charges inside a metal. Therefore, it should be noted that electrons inside a metal must move continuously. This is the very basic definition of the current, a non-equilibrium system in which there is a constant flow of electrons in order to create a magnetic field.

There are a few important main concepts to understand before proceeding further. First, the direction of the magnetic field is perpendicular to the direction of the current. Second, equilibrium and being continuous are totally different things.

===A Mathematical Model===
The magnetic field created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savart law. You may notice that this equation involves a cross product.

== characteristics of the Biot-Savart Law==
Because the equation involves the cross product of velocity and the position vector, one can find out that there is no magnetic field in the direction of the movement of the charged particle, because the cross product of two vectors in the same direction is zero.

However, even in the absence of a magnetic field, an electric field may still be present.

By using a compass, one can calculate the magnitude of a current. The Earth exerts a magnitude that always points to the North. When a compass is near a current with a magnetic field, the needle would be deflected by the net magnetic field. Notice that although the magnetic field of the current is perpendicular to the direction of the movement of charges, the needle is not deflected 90 degrees because of the magnetic field of the Earth, which is usually larger than that of the current. Also, because the magnetic field is exerted in a circular pattern, the direction of the magnetic field above the source is exactly the opposite of the magnetic field under the source. As a result, depending on the location of the compass, the needle may deflect in the opposite direction but with the same magnitude.

== Dependence on frame of reference== (<math> \vec{v} = 0</math>)

== Magnetic field due to a single charged particle==

The magnetic field <math> \vec{B}</math> created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savarde law. You may notice that this equation involves a cross product.

Page initiated by --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 14:20, 19 October 2015 (EDT)
[[Category: Fields]]

Magnetic Field

2016-04-18T00:20:11Z

Skim773:

Magnetic Field

2016-04-18T00:15:13Z

Skim773:

Magnetic Field

2016-04-18T00:09:05Z

Skim773:

Claimed by Seongshik Kim spring 2016

This page discusses the general properties of magnetic fields

== Magnetic Field==

Magnetic Field is a [[field]] created by a moving electric charge. It is measured in units of Teslas (T) and has a direction, making it a vector quantity. The magnetic field created by a moving charge exists at all points in space and exerts a force on other charged objects. The field can be drawn as an arrow with tail at the observation location pointing in the direction of the field. The magnetic field obeys superposition, so the net magnetic field at a point in space can be determined by summing all the individual fields present at that location.

== Dependence on frame of reference==

Because the magnetic field relies on the velocity of a particle, it can vary with frame of reference. That is to say, one observer could observe a magnetic field while another does not observe a field due to the relative velocity of the particle. Consider a moving proton, a moving compass, and a stationary compass. The proton and moving compass are moving with identical velocity, so to the compass, the proton appears to be stationary (<math> \vec{v} = 0</math>), so the observed magnetic field is is also 0. The stationary compass, however, observes a certain velocity so a magnetic field is observed.

== Magnetic field due to a single charged particle==

The magnetic field <math> \vec{B}</math> created by a single charged particle is given by the equation <math> \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|\vec{r}|^2} </math>, where <math> \frac{\mu_0}{4\pi}</math> is a fundamental constant equal to <math> 1 \times 10^{-7} T </math>, <math>q</math> is the charge of the particle, <math> \vec{v}</math> is the velocity of the particle, and <math> \vec{r}</math> is the vector that points from source to observation location. This equation is called the Biot-Savarde law. You may notice that this equation involves a cross product.

Page initiated by --[[User:Spennell3|Spennell3]] ([[User talk:Spennell3|talk]]) 14:20, 19 October 2015 (EDT)
[[Category: Fields]]