Physics Book - User contributions [en]

Bar Magnet

2016-04-18T01:54:39Z

Shisamuddin3:

claimed by Samah

A bar magnet creates a magnetic field, just like many other devices (i.e. a current carrying wire), however, it has a different pattern of magnetic field which we will explore.

__TOC__

== '''The Main Idea''' ==
----
The main idea for this topic is to explore how a bar magnet works and the effects that it has on its surroundings.

== '''A Mathematical Model''' ==
----

In physics it is important to keep track of your frame of reference. Treat an effect as if it is arising at the source location and ending at the observation location. The source location marks the beginning point for an effect. The result of the effect is gauged at the observation location.

Due to the fact that an observation location can either be on the axis of the magnet, or off the axis of the magnet, we have to different equations. For an observation location that is on the same axis as the magnet, assuming that the distance from the observation location to the magnet is much greater than the the separation distance of the two poles we find that:
<math> B = \frac{\mu _{0}}{4\pi }\cdot \frac{2\mu }{r^{3}}</math>

If the observation location is not on the axis of the bar magnet, and assuming that the distance from the observation location to the magnet is less than the the separation distance of the two poles we conclude that:
<math> B = \frac{\mu _{0}}{4\pi }\cdot \frac{\mu }{r^{3}}</math>

== '''A Computational Model''' ==
----
[[File:VFPt cylindrical magnet thumb.svg|thumb|left|The curly magnetic field of a bar magnet.]]

As you can see in this picture, the magnetic field of a bar magnet takes the exact same form as an electric field of a dipole. The magnetic lines flow out of the north pole to the magnet, and into the south pole of the magnet, in a curling fashion. However, the 'poles' are merely just conventions. They do not represent anything, and are terms just assigned to each end, but it is true that the magnetic field will always flow out of the 'north end'. Like a bar magnet, the Earth itself can also be represented by the computational model of a bar magnet, however, there are a few misconceptions about this. For starters, the magnetic North Pole is actually located at the geographic South Pole, and the magnetic South Pole is located at the geographic North Pole. Furthermore, the magnetic poles are off axis, meaning the are not directly at the top and bottom of the Earth. There is a difference of almost 1.5 degrees!
It is also interesting to note that just because this illustration depicts the bar magnet as having two distinct ends, if you were to cut the magnet down the middle, you would assume that you would end up with a south end and a north end. However, this is not the case. If a magnet were to be cut in half, it would polarize in such a way that you would end up with two bar magnets, not a single south pole and a single north pole.

[[File:Magnet0873.png|thumb|left|The magnetic field of a bar magnet.]]

This picture depicts the magnetic field based on the dipoles of the magnet. The north end is on the left side of the magnet and the south end is on the right side of the magnet. The field follows the direction from the north side to the south side of the magnet.

== '''Examples''' ==
----
'''Example 1''': If a bar magnet is located at the origin aligned with its North end aligned with the positive X-axis, what are the directions of the magnetic field at the following observation locations: above, below, to the left, to the right, and in a plane that is above the magnet?

Well, we already know that the field of a bar magnet flows out of the north end and into the south end in a curling fashion. So, using the diagram above, it is easy to see that to the right of the magnet, the direction of the magnetic field points in the +X direction. At a position to the left of the magnet, the field is flowing back into the south end of the magnet, so the direction of the magnetic field at this location is ALSO in the +X direction.

The field above and below the magnet is flowing from the right to the left at both locations, so the direction of the magnetic field above and below the magnet is in the -X direction.

At a different plane (z doesn't = 0), there is no magnetic field, because we can assume that bar magnet acts as a 2-D dipole.

'''Example 2:''' A bar magnet with magnetic dipole moment 0.58 lies on the negative x axis, as shown in the figure below. A compass is located at the origin. Magnetic north is in the negative z direction. Between the bar magnet and the compass is a coil of wire of radius 3.5 cm, connected to batteries not shown. The distance from the center of the coil to the center of the compass is 9.6 cm. The distance from the center of the bar magnet to the center of the compass is 23.0 cm. A steady current of 0.96 A runs through the coil. Conventional current runs clockwise in the coil when viewed from the location of the compass. Despite the presence of the magnet and coil the compass still points north.

'''(a)''' Which end of the bar magnet is closest to the compass?
'''(b)''' How many turns of wire are in the coil?

'''Part A:''' Because the conventional current runs clockwise in the coil, you can use right hand rule to determine what direction the magnetic field is due to the coil. This tells us that the magnetic field due to the coil is in the -X direction. In order for the compass to stay still, the magnet needs to directly oppose the magnetic field of the coil, meaning its magnetic field has to point in the +X direction, meaning the '''NORTH end''' would have to be nearest the compass (because the field flows out of the north end into the positive end).

'''Part B:''' Because the field created by the coil equals the field created by the magnet, we can set their two fields equal to each other:
<math> \frac{\mu _{0}}{4 \pi } \cdot \frac{2\mu }{r^{3}} = \frac{\mu _{0}}{4 \pi } \cdot \frac{2NI\pi R^{2}}{(z^{2}+R^{2})^{3/2}} </math>

Rearranging to solve this equation for N, we get: <math> N = \frac{\mu (z^{2}+R^{2})^{3/2}}{I\pi R^{2} d^{3}} </math>

Plugging in .58 the magnetic dipole moment (mu), .096 meters for z, .035 meters for R, .96 Amps for I, and .23 meters for d, we get that the number of loops in the coil is '''14.'''

== '''Connectedness''' ==
----
[[File:Series L0.JPG|thumb|left|An experimental MAGLEV train created by Japanese engineers.]]
One very interesting applications of magnets is their ability to levitate objects. This is the main driving force in the case of MAGLEV trains. Magnetic levitation, or MAGLEV trains, hover above a long series of magnets where the magnets on the bottom of the train repel the magnets on the tracks below it. Sending an electric current through the coils on the bottom of the track allows the train to levitate a few inches off the ground, and propelling the current through the guided coils on the bottom of the track propels the train forward at unbelievable speeds (up to 250 MPH!).

Making the train levitate is a useful tool because it reduces the amount of friction between the wheels and the track, and it allows for less fossil fuels to be used in order to make the train propel forwards.

[[File:img.jpg|thumb|left|MRI of brain.]]
Magnetism is also used in medical technology. Medical resonance imaging (MRIs) machines use magnetic fields and radio waves to create images of the body.

== '''History''' ==
----
[[File:James Clerk Maxwell.png|thumb|right|James Clerk Maxwell]]
The first magnets were not invented, but rather discovered. The ancient Greeks and ancient Chinese peoples stumbled upon a naturally occurring material, called magnetite, by mistake. People were so astounded by it that tales were told of magical islands where magnetic nature was everywhere. The Chinese actually developed a compass around 4500 years using this magnetite!

Despite not being the first people to study magnetism, Hans Christian Oersted did prove that electricity and magnetism were related by bringing a current carrying wire close to a compass needle. However, it wasn't until Maxwell published his findings in 1862 that led to the relationships between electricity and magnetism (Maxwell's Equations; see other Wikipedia page).

== '''External links''' ==
----
# MAGLEV Trains: http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Magnetism-Real-life-applications.html
# More information on Bar Magnets: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html

== '''References''' ==
----
# http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html
# https://en.wikipedia.org/wiki/Magnet#/media/File:VFPt_cylindrical_magnet_thumb.svg
# http://www.howmagnetswork.com/history.html
# https://en.wikipedia.org/wiki/Maglev#/media/File:Series_L0.JPG
# https://en.wikipedia.org/wiki/James_Clerk_Maxwell#/media/File:James_Clerk_Maxwell.png
Category: '''Fields'''

'''Created by: John Joyce'''

__FORCETOC__

Bar Magnet

2016-04-18T01:50:59Z

Shisamuddin3:

claimed by Samah

A bar magnet creates a magnetic field, just like many other devices (i.e. a current carrying wire), however, it has a different pattern of magnetic field which we will explore.

__TOC__

== '''The Main Idea''' ==
----
The main idea for this topic is to explore how a bar magnet works and the effects that it has on its surroundings.

== '''A Mathematical Model''' ==
----

In physics it is important to keep track of your frame of reference. Treat an effect as if it is arising at the source location and ending at the observation location. The source location marks the beginning point for an effect. The result of the effect is gauged at the observation location.

Due to the fact that an observation location can either be on the axis of the magnet, or off the axis of the magnet, we have to different equations. For an observation location that is on the same axis as the magnet, assuming that the distance from the observation location to the magnet is much greater than the the separation distance of the two poles we find that:
<math> B = \frac{\mu _{0}}{4\pi }\cdot \frac{2\mu }{r^{3}}</math>

If the observation location is not on the axis of the bar magnet, and assuming that the distance from the observation location to the magnet is less than the the separation distance of the two poles we conclude that:
<math> B = \frac{\mu _{0}}{4\pi }\cdot \frac{\mu }{r^{3}}</math>

== '''A Computational Model''' ==
----
[[File:VFPt cylindrical magnet thumb.svg|thumb|left|The curly magnetic field of a bar magnet.]]

As you can see in this picture, the magnetic field of a bar magnet takes the exact same form as an electric field of a dipole. The magnetic lines flow out of the north pole to the magnet, and into the south pole of the magnet, in a curling fashion. However, the 'poles' are merely just conventions. They do not represent anything, and are terms just assigned to each end, but it is true that the magnetic field will always flow out of the 'north end'. Like a bar magnet, the Earth itself can also be represented by the computational model of a bar magnet, however, there are a few misconceptions about this. For starters, the magnetic North Pole is actually located at the geographic South Pole, and the magnetic South Pole is located at the geographic North Pole. Furthermore, the magnetic poles are off axis, meaning the are not directly at the top and bottom of the Earth. There is a difference of almost 1.5 degrees!
It is also interesting to note that just because this illustration depicts the bar magnet as having two distinct ends, if you were to cut the magnet down the middle, you would assume that you would end up with a south end and a north end. However, this is not the case. If a magnet were to be cut in half, it would polarize in such a way that you would end up with two bar magnets, not a single south pole and a single north pole.

[[File:Magnet0873.png|thumb|left|The magnetic field of a bar magnet.]]

This picture depicts the magnetic field based on the dipoles of the magnet. The north end is on the left side of the magnet and the south end is on the right side of the magnet. The field follows the direction from the north side to the south side of the magnet.

== '''Examples''' ==
----
'''Example 1''': If a bar magnet is located at the origin aligned with its North end aligned with the positive X-axis, what are the directions of the magnetic field at the following observation locations: above, below, to the left, to the right, and in a plane that is above the magnet?

Well, we already know that the field of a bar magnet flows out of the north end and into the south end in a curling fashion. So, using the diagram above, it is easy to see that to the right of the magnet, the direction of the magnetic field points in the +X direction. At a position to the left of the magnet, the field is flowing back into the south end of the magnet, so the direction of the magnetic field at this location is ALSO in the +X direction.

The field above and below the magnet is flowing from the right to the left at both locations, so the direction of the magnetic field above and below the magnet is in the -X direction.

At a different plane (z doesn't = 0), there is no magnetic field, because we can assume that bar magnet acts as a 2-D dipole.

'''Example 2:''' A bar magnet with magnetic dipole moment 0.58 lies on the negative x axis, as shown in the figure below. A compass is located at the origin. Magnetic north is in the negative z direction. Between the bar magnet and the compass is a coil of wire of radius 3.5 cm, connected to batteries not shown. The distance from the center of the coil to the center of the compass is 9.6 cm. The distance from the center of the bar magnet to the center of the compass is 23.0 cm. A steady current of 0.96 A runs through the coil. Conventional current runs clockwise in the coil when viewed from the location of the compass. Despite the presence of the magnet and coil the compass still points north.

'''(a)''' Which end of the bar magnet is closest to the compass?
'''(b)''' How many turns of wire are in the coil?

'''Part A:''' Because the conventional current runs clockwise in the coil, you can use right hand rule to determine what direction the magnetic field is due to the coil. This tells us that the magnetic field due to the coil is in the -X direction. In order for the compass to stay still, the magnet needs to directly oppose the magnetic field of the coil, meaning its magnetic field has to point in the +X direction, meaning the '''NORTH end''' would have to be nearest the compass (because the field flows out of the north end into the positive end).

'''Part B:''' Because the field created by the coil equals the field created by the magnet, we can set their two fields equal to each other:
<math> \frac{\mu _{0}}{4 \pi } \cdot \frac{2\mu }{r^{3}} = \frac{\mu _{0}}{4 \pi } \cdot \frac{2NI\pi R^{2}}{(z^{2}+R^{2})^{3/2}} </math>

Rearranging to solve this equation for N, we get: <math> N = \frac{\mu (z^{2}+R^{2})^{3/2}}{I\pi R^{2} d^{3}} </math>

Plugging in .58 the magnetic dipole moment (mu), .096 meters for z, .035 meters for R, .96 Amps for I, and .23 meters for d, we get that the number of loops in the coil is '''14.'''

== '''Connectedness''' ==
----
[[File:Series L0.JPG|thumb|left|An experimental MAGLEV train created by Japanese engineers.]]
One very interesting applications of magnets is their ability to levitate objects. This is the main driving force in the case of MAGLEV trains. Magnetic levitation, or MAGLEV trains, hover above a long series of magnets where the magnets on the bottom of the train repel the magnets on the tracks below it. Sending an electric current through the coils on the bottom of the track allows the train to levitate a few inches off the ground, and propelling the current through the guided coils on the bottom of the track propels the train forward at unbelievable speeds (up to 250 MPH!).

Making the train levitate is a useful tool because it reduces the amount of friction between the wheels and the track, and it allows for less fossil fuels to be used in order to make the train propel forwards.

Magnetism is also used in medical technology. Medical resonance imaging (MRIs) machines use magnetic fields and radio waves to create images of the body.

== '''History''' ==
----
[[File:James Clerk Maxwell.png|thumb|right|James Clerk Maxwell]]
The first magnets were not invented, but rather discovered. The ancient Greeks and ancient Chinese peoples stumbled upon a naturally occurring material, called magnetite, by mistake. People were so astounded by it that tales were told of magical islands where magnetic nature was everywhere. The Chinese actually developed a compass around 4500 years using this magnetite!

Despite not being the first people to study magnetism, Hans Christian Oersted did prove that electricity and magnetism were related by bringing a current carrying wire close to a compass needle. However, it wasn't until Maxwell published his findings in 1862 that led to the relationships between electricity and magnetism (Maxwell's Equations; see other Wikipedia page).

== '''External links''' ==
----
# MAGLEV Trains: http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Magnetism-Real-life-applications.html
# More information on Bar Magnets: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html

== '''References''' ==
----
# http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html
# https://en.wikipedia.org/wiki/Magnet#/media/File:VFPt_cylindrical_magnet_thumb.svg
# http://www.howmagnetswork.com/history.html
# https://en.wikipedia.org/wiki/Maglev#/media/File:Series_L0.JPG
# https://en.wikipedia.org/wiki/James_Clerk_Maxwell#/media/File:James_Clerk_Maxwell.png
Category: '''Fields'''

'''Created by: John Joyce'''

__FORCETOC__

Bar Magnet

2016-04-18T01:44:16Z

Shisamuddin3:

claimed by Samah

A bar magnet creates a magnetic field, just like many other devices (i.e. a current carrying wire), however, it has a different pattern of magnetic field which we will explore.

__TOC__

== '''The Main Idea''' ==
----
The main idea for this topic is to explore how a bar magnet works and the effects that it has on its surroundings.

== '''A Mathematical Model''' ==
----

In physics it is important to keep track of your frame of reference. Treat an effect as if it is arising at the source location and ending at the observation location. The source location marks the beginning point for an effect. The result of the effect is gauged at the observation location.

Due to the fact that an observation location can either be on the axis of the magnet, or off the axis of the magnet, we have to different equations. For an observation location that is on the same axis as the magnet, assuming that the distance from the observation location to the magnet is much greater than the the separation distance of the two poles we find that:
<math> B = \frac{\mu _{0}}{4\pi }\cdot \frac{2\mu }{r^{3}}</math>

If the observation location is not on the axis of the bar magnet, and assuming that the distance from the observation location to the magnet is less than the the separation distance of the two poles we conclude that:
<math> B = \frac{\mu _{0}}{4\pi }\cdot \frac{\mu }{r^{3}}</math>

== '''A Computational Model''' ==
----
[[File:VFPt cylindrical magnet thumb.svg|thumb|left|The curly magnetic field of a bar magnet.]]

As you can see in this picture, the magnetic field of a bar magnet takes the exact same form as an electric field of a dipole. The magnetic lines flow out of the north pole to the magnet, and into the south pole of the magnet, in a curling fashion. However, the 'poles' are merely just conventions. They do not represent anything, and are terms just assigned to each end, but it is true that the magnetic field will always flow out of the 'north end'. Like a bar magnet, the Earth itself can also be represented by the computational model of a bar magnet, however, there are a few misconceptions about this. For starters, the magnetic North Pole is actually located at the geographic South Pole, and the magnetic South Pole is located at the geographic North Pole. Furthermore, the magnetic poles are off axis, meaning the are not directly at the top and bottom of the Earth. There is a difference of almost 1.5 degrees!
It is also interesting to note that just because this illustration depicts the bar magnet as having two distinct ends, if you were to cut the magnet down the middle, you would assume that you would end up with a south end and a north end. However, this is not the case. If a magnet were to be cut in half, it would polarize in such a way that you would end up with two bar magnets, not a single south pole and a single north pole.

[[File:Magnet0873.png|thumb|left|The magnetic field of a bar magnet.]]

This picture depicts the magnetic field based on the dipoles of the magnet. The north end is on the left side of the magnet and the south end is on the right side of the magnet. The field follows the direction from the north side to the south side of the magnet.

== '''Examples''' ==
----
'''Example 1''': If a bar magnet is located at the origin aligned with its North end aligned with the positive X-axis, what are the directions of the magnetic field at the following observation locations: above, below, to the left, to the right, and in a plane that is above the magnet?

Well, we already know that the field of a bar magnet flows out of the north end and into the south end in a curling fashion. So, using the diagram above, it is easy to see that to the right of the magnet, the direction of the magnetic field points in the +X direction. At a position to the left of the magnet, the field is flowing back into the south end of the magnet, so the direction of the magnetic field at this location is ALSO in the +X direction.

The field above and below the magnet is flowing from the right to the left at both locations, so the direction of the magnetic field above and below the magnet is in the -X direction.

At a different plane (z doesn't = 0), there is no magnetic field, because we can assume that bar magnet acts as a 2-D dipole.

'''Example 2:''' A bar magnet with magnetic dipole moment 0.58 lies on the negative x axis, as shown in the figure below. A compass is located at the origin. Magnetic north is in the negative z direction. Between the bar magnet and the compass is a coil of wire of radius 3.5 cm, connected to batteries not shown. The distance from the center of the coil to the center of the compass is 9.6 cm. The distance from the center of the bar magnet to the center of the compass is 23.0 cm. A steady current of 0.96 A runs through the coil. Conventional current runs clockwise in the coil when viewed from the location of the compass. Despite the presence of the magnet and coil the compass still points north.

'''(a)''' Which end of the bar magnet is closest to the compass?
'''(b)''' How many turns of wire are in the coil?

'''Part A:''' Because the conventional current runs clockwise in the coil, you can use right hand rule to determine what direction the magnetic field is due to the coil. This tells us that the magnetic field due to the coil is in the -X direction. In order for the compass to stay still, the magnet needs to directly oppose the magnetic field of the coil, meaning its magnetic field has to point in the +X direction, meaning the '''NORTH end''' would have to be nearest the compass (because the field flows out of the north end into the positive end).

'''Part B:''' Because the field created by the coil equals the field created by the magnet, we can set their two fields equal to each other:
<math> \frac{\mu _{0}}{4 \pi } \cdot \frac{2\mu }{r^{3}} = \frac{\mu _{0}}{4 \pi } \cdot \frac{2NI\pi R^{2}}{(z^{2}+R^{2})^{3/2}} </math>

Rearranging to solve this equation for N, we get: <math> N = \frac{\mu (z^{2}+R^{2})^{3/2}}{I\pi R^{2} d^{3}} </math>

Plugging in .58 the magnetic dipole moment (mu), .096 meters for z, .035 meters for R, .96 Amps for I, and .23 meters for d, we get that the number of loops in the coil is '''14.'''

== '''Connectedness''' ==
----
[[File:Series L0.JPG|thumb|left|An experimental MAGLEV train created by Japanese engineers.]]
One very interesting applications of magnets is their ability to levitate objects. This is the main driving force in the case of MAGLEV trains. Magnetic levitation, or MAGLEV trains, hover above a long series of magnets where the magnets on the bottom of the train repel the magnets on the tracks below it. Sending an electric current through the coils on the bottom of the track allows the train to levitate a few inches off the ground, and propelling the current through the guided coils on the bottom of the track propels the train forward at unbelievable speeds (up to 250 MPH!).

Making the train levitate is a useful tool because it reduces the amount of friction between the wheels and the track, and it allows for less fossil fuels to be used in order to make the train propel forwards.

== '''History''' ==
----
[[File:James Clerk Maxwell.png|thumb|right|James Clerk Maxwell]]
The first magnets were not invented, but rather discovered. The ancient Greeks and ancient Chinese peoples stumbled upon a naturally occurring material, called magnetite, by mistake. People were so astounded by it that tales were told of magical islands where magnetic nature was everywhere. The Chinese actually developed a compass around 4500 years using this magnetite!

Despite not being the first people to study magnetism, Hans Christian Oersted did prove that electricity and magnetism were related by bringing a current carrying wire close to a compass needle. However, it wasn't until Maxwell published his findings in 1862 that led to the relationships between electricity and magnetism (Maxwell's Equations; see other Wikipedia page).

== '''External links''' ==
----
# MAGLEV Trains: http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Magnetism-Real-life-applications.html
# More information on Bar Magnets: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html

== '''References''' ==
----
# http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html
# https://en.wikipedia.org/wiki/Magnet#/media/File:VFPt_cylindrical_magnet_thumb.svg
# http://www.howmagnetswork.com/history.html
# https://en.wikipedia.org/wiki/Maglev#/media/File:Series_L0.JPG
# https://en.wikipedia.org/wiki/James_Clerk_Maxwell#/media/File:James_Clerk_Maxwell.png
Category: '''Fields'''

'''Created by: John Joyce'''

__FORCETOC__

Bar Magnet

2016-04-18T01:39:34Z

Shisamuddin3:

claimed by Samah

A bar magnet creates a magnetic field, just like many other devices (i.e. a current carrying wire), however, it has a different pattern of magnetic field which we will explore.

__TOC__

== '''The Main Idea''' ==
----
The main idea for this topic is to explore how a bar magnet works and the effects that it has on its surroundings.

== '''A Mathematical Model''' ==
----

In physics it is important to keep track of your frame of reference. Treat an effect as if it is arising at the source location and ending at the observation location. The source location marks the beginning point for an effect. The result of the effect is gauged at the observation location.

Due to the fact that an observation location can either be on the axis of the magnet, or off the axis of the magnet, we have to different equations. For an observation location that is on the same axis as the magnet, assuming that the distance from the observation location to the magnet is much greater than the the separation distance of the two poles we find that:
<math> B = \frac{\mu _{0}}{4\pi }\cdot \frac{2\mu }{r^{3}}</math>

If the observation location is not on the axis of the bar magnet, and assuming that the distance from the observation location to the magnet is less than the the separation distance of the two poles we conclude that:
<math> B = \frac{\mu _{0}}{4\pi }\cdot \frac{\mu }{r^{3}}</math>

== '''A Computational Model''' ==
----
[[File:VFPt cylindrical magnet thumb.svg|thumb|left|The curly magnetic field of a bar magnet.]]

As you can see in this picture, the magnetic field of a bar magnet takes the exact same form as an electric field of a dipole. The magnetic lines flow out of the north pole to the magnet, and into the south pole of the magnet, in a curling fashion. However, the 'poles' are merely just conventions. They do not represent anything, and are terms just assigned to each end, but it is true that the magnetic field will always flow out of the 'north end'. Like a bar magnet, the Earth itself can also be represented by the computational model of a bar magnet, however, there are a few misconceptions about this. For starters, the magnetic North Pole is actually located at the geographic South Pole, and the magnetic South Pole is located at the geographic North Pole. Furthermore, the magnetic poles are off axis, meaning the are not directly at the top and bottom of the Earth. There is a difference of almost 1.5 degrees!
It is also interesting to note that just because this illustration depicts the bar magnet as having two distinct ends, if you were to cut the magnet down the middle, you would assume that you would end up with a south end and a north end. However, this is not the case. If a magnet were to be cut in half, it would polarize in such a way that you would end up with two bar magnets, not a single south pole and a single north pole.

[[File:Magnet0873.png|thumb|left|The electric field of a bar magnet.]]

== '''Examples''' ==
----
'''Example 1''': If a bar magnet is located at the origin aligned with its North end aligned with the positive X-axis, what are the directions of the magnetic field at the following observation locations: above, below, to the left, to the right, and in a plane that is above the magnet?

Well, we already know that the field of a bar magnet flows out of the north end and into the south end in a curling fashion. So, using the diagram above, it is easy to see that to the right of the magnet, the direction of the magnetic field points in the +X direction. At a position to the left of the magnet, the field is flowing back into the south end of the magnet, so the direction of the magnetic field at this location is ALSO in the +X direction.

The field above and below the magnet is flowing from the right to the left at both locations, so the direction of the magnetic field above and below the magnet is in the -X direction.

At a different plane (z doesn't = 0), there is no magnetic field, because we can assume that bar magnet acts as a 2-D dipole.

'''Example 2:''' A bar magnet with magnetic dipole moment 0.58 lies on the negative x axis, as shown in the figure below. A compass is located at the origin. Magnetic north is in the negative z direction. Between the bar magnet and the compass is a coil of wire of radius 3.5 cm, connected to batteries not shown. The distance from the center of the coil to the center of the compass is 9.6 cm. The distance from the center of the bar magnet to the center of the compass is 23.0 cm. A steady current of 0.96 A runs through the coil. Conventional current runs clockwise in the coil when viewed from the location of the compass. Despite the presence of the magnet and coil the compass still points north.

'''(a)''' Which end of the bar magnet is closest to the compass?
'''(b)''' How many turns of wire are in the coil?

'''Part A:''' Because the conventional current runs clockwise in the coil, you can use right hand rule to determine what direction the magnetic field is due to the coil. This tells us that the magnetic field due to the coil is in the -X direction. In order for the compass to stay still, the magnet needs to directly oppose the magnetic field of the coil, meaning its magnetic field has to point in the +X direction, meaning the '''NORTH end''' would have to be nearest the compass (because the field flows out of the north end into the positive end).

'''Part B:''' Because the field created by the coil equals the field created by the magnet, we can set their two fields equal to each other:
<math> \frac{\mu _{0}}{4 \pi } \cdot \frac{2\mu }{r^{3}} = \frac{\mu _{0}}{4 \pi } \cdot \frac{2NI\pi R^{2}}{(z^{2}+R^{2})^{3/2}} </math>

Rearranging to solve this equation for N, we get: <math> N = \frac{\mu (z^{2}+R^{2})^{3/2}}{I\pi R^{2} d^{3}} </math>

Plugging in .58 the magnetic dipole moment (mu), .096 meters for z, .035 meters for R, .96 Amps for I, and .23 meters for d, we get that the number of loops in the coil is '''14.'''

== '''Connectedness''' ==
----
[[File:Series L0.JPG|thumb|left|An experimental MAGLEV train created by Japanese engineers.]]
One very interesting applications of magnets is their ability to levitate objects. This is the main driving force in the case of MAGLEV trains. Magnetic levitation, or MAGLEV trains, hover above a long series of magnets where the magnets on the bottom of the train repel the magnets on the tracks below it. Sending an electric current through the coils on the bottom of the track allows the train to levitate a few inches off the ground, and propelling the current through the guided coils on the bottom of the track propels the train forward at unbelievable speeds (up to 250 MPH!).

Making the train levitate is a useful tool because it reduces the amount of friction between the wheels and the track, and it allows for less fossil fuels to be used in order to make the train propel forwards.

== '''History''' ==
----
[[File:James Clerk Maxwell.png|thumb|right|James Clerk Maxwell]]
The first magnets were not invented, but rather discovered. The ancient Greeks and ancient Chinese peoples stumbled upon a naturally occurring material, called magnetite, by mistake. People were so astounded by it that tales were told of magical islands where magnetic nature was everywhere. The Chinese actually developed a compass around 4500 years using this magnetite!

Despite not being the first people to study magnetism, Hans Christian Oersted did prove that electricity and magnetism were related by bringing a current carrying wire close to a compass needle. However, it wasn't until Maxwell published his findings in 1862 that led to the relationships between electricity and magnetism (Maxwell's Equations; see other Wikipedia page).

== '''External links''' ==
----
# MAGLEV Trains: http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Magnetism-Real-life-applications.html
# More information on Bar Magnets: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html

== '''References''' ==
----
# http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html
# https://en.wikipedia.org/wiki/Magnet#/media/File:VFPt_cylindrical_magnet_thumb.svg
# http://www.howmagnetswork.com/history.html
# https://en.wikipedia.org/wiki/Maglev#/media/File:Series_L0.JPG
# https://en.wikipedia.org/wiki/James_Clerk_Maxwell#/media/File:James_Clerk_Maxwell.png
Category: '''Fields'''

'''Created by: John Joyce'''

__FORCETOC__

Bar Magnet

2016-04-18T01:27:48Z

Shisamuddin3:

claimed by Samah

A bar magnet creates a magnetic field, just like many other devices (i.e. a current carrying wire), however, it has a different pattern of magnetic field which we will explore.

__TOC__

== '''The Main Idea''' ==
----
The main idea for this topic is to explore how a bar magnet works and the effects that it has on its surroundings.

== '''A Mathematical Model''' ==
----

In physics it is important to keep track of your frame of reference. Treat an effect as if it is arising at the source location and ending at the observation location. The source location marks the beginning point for an effect. The result of the effect is gauged at the observation location.

Due to the fact that an observation location can either be on the axis of the magnet, or off the axis of the magnet, we have to different equations. For an observation location that is on the same axis as the magnet, assuming that the distance from the observation location to the magnet is much greater than the the separation distance of the two poles we find that:
<math> B = \frac{\mu _{0}}{4\pi }\cdot \frac{2\mu }{r^{3}}</math>

If the observation location is not on the axis of the bar magnet, and assuming that the distance from the observation location to the magnet is less than the the separation distance of the two poles we conclude that:
<math> B = \frac{\mu _{0}}{4\pi }\cdot \frac{\mu }{r^{3}}</math>

== '''A Computational Model''' ==
----
[[File:VFPt cylindrical magnet thumb.svg|thumb|left|The curly magnetic field of a bar magnet.]]

As you can see in this picture, the magnetic field of a bar magnet takes the exact same form as an electric field of a dipole. The magnetic lines flow out of the north pole to the magnet, and into the south pole of the magnet, in a curling fashion. However, the 'poles' are merely just conventions. They do not represent anything, and are terms just assigned to each end, but it is true that the magnetic field will always flow out of the 'north end'. Like a bar magnet, the Earth itself can also be represented by the computational model of a bar magnet, however, there are a few misconceptions about this. For starters, the magnetic North Pole is actually located at the geographic South Pole, and the magnetic South Pole is located at the geographic North Pole. Furthermore, the magnetic poles are off axis, meaning the are not directly at the top and bottom of the Earth. There is a difference of almost 1.5 degrees!
It is also interesting to note that just because this illustration depicts the bar magnet as having two distinct ends, if you were to cut the magnet down the middle, you would assume that you would end up with a south end and a north end. However, this is not the case. If a magnet were to be cut in half, it would polarize in such a way that you would end up with two bar magnets, not a single south pole and a single north pole.

== '''Examples''' ==
----
'''Example 1''': If a bar magnet is located at the origin aligned with its North end aligned with the positive X-axis, what are the directions of the magnetic field at the following observation locations: above, below, to the left, to the right, and in a plane that is above the magnet?

Well, we already know that the field of a bar magnet flows out of the north end and into the south end in a curling fashion. So, using the diagram above, it is easy to see that to the right of the magnet, the direction of the magnetic field points in the +X direction. At a position to the left of the magnet, the field is flowing back into the south end of the magnet, so the direction of the magnetic field at this location is ALSO in the +X direction.

The field above and below the magnet is flowing from the right to the left at both locations, so the direction of the magnetic field above and below the magnet is in the -X direction.

At a different plane (z doesn't = 0), there is no magnetic field, because we can assume that bar magnet acts as a 2-D dipole.

'''Example 2:''' A bar magnet with magnetic dipole moment 0.58 lies on the negative x axis, as shown in the figure below. A compass is located at the origin. Magnetic north is in the negative z direction. Between the bar magnet and the compass is a coil of wire of radius 3.5 cm, connected to batteries not shown. The distance from the center of the coil to the center of the compass is 9.6 cm. The distance from the center of the bar magnet to the center of the compass is 23.0 cm. A steady current of 0.96 A runs through the coil. Conventional current runs clockwise in the coil when viewed from the location of the compass. Despite the presence of the magnet and coil the compass still points north.

'''(a)''' Which end of the bar magnet is closest to the compass?
'''(b)''' How many turns of wire are in the coil?

'''Part A:''' Because the conventional current runs clockwise in the coil, you can use right hand rule to determine what direction the magnetic field is due to the coil. This tells us that the magnetic field due to the coil is in the -X direction. In order for the compass to stay still, the magnet needs to directly oppose the magnetic field of the coil, meaning its magnetic field has to point in the +X direction, meaning the '''NORTH end''' would have to be nearest the compass (because the field flows out of the north end into the positive end).

'''Part B:''' Because the field created by the coil equals the field created by the magnet, we can set their two fields equal to each other:
<math> \frac{\mu _{0}}{4 \pi } \cdot \frac{2\mu }{r^{3}} = \frac{\mu _{0}}{4 \pi } \cdot \frac{2NI\pi R^{2}}{(z^{2}+R^{2})^{3/2}} </math>

Rearranging to solve this equation for N, we get: <math> N = \frac{\mu (z^{2}+R^{2})^{3/2}}{I\pi R^{2} d^{3}} </math>

Plugging in .58 the magnetic dipole moment (mu), .096 meters for z, .035 meters for R, .96 Amps for I, and .23 meters for d, we get that the number of loops in the coil is '''14.'''

== '''Connectedness''' ==
----
[[File:Series L0.JPG|thumb|left|An experimental MAGLEV train created by Japanese engineers.]]
One very interesting applications of magnets is their ability to levitate objects. This is the main driving force in the case of MAGLEV trains. Magnetic levitation, or MAGLEV trains, hover above a long series of magnets where the magnets on the bottom of the train repel the magnets on the tracks below it. Sending an electric current through the coils on the bottom of the track allows the train to levitate a few inches off the ground, and propelling the current through the guided coils on the bottom of the track propels the train forward at unbelievable speeds (up to 250 MPH!).

Making the train levitate is a useful tool because it reduces the amount of friction between the wheels and the track, and it allows for less fossil fuels to be used in order to make the train propel forwards.

== '''History''' ==
----
[[File:James Clerk Maxwell.png|thumb|right|James Clerk Maxwell]]
The first magnets were not invented, but rather discovered. The ancient Greeks and ancient Chinese peoples stumbled upon a naturally occurring material, called magnetite, by mistake. People were so astounded by it that tales were told of magical islands where magnetic nature was everywhere. The Chinese actually developed a compass around 4500 years using this magnetite!

Despite not being the first people to study magnetism, Hans Christian Oersted did prove that electricity and magnetism were related by bringing a current carrying wire close to a compass needle. However, it wasn't until Maxwell published his findings in 1862 that led to the relationships between electricity and magnetism (Maxwell's Equations; see other Wikipedia page).

== '''External links''' ==
----
# MAGLEV Trains: http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Magnetism-Real-life-applications.html
# More information on Bar Magnets: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html

== '''References''' ==
----
# http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html
# https://en.wikipedia.org/wiki/Magnet#/media/File:VFPt_cylindrical_magnet_thumb.svg
# http://www.howmagnetswork.com/history.html
# https://en.wikipedia.org/wiki/Maglev#/media/File:Series_L0.JPG
# https://en.wikipedia.org/wiki/James_Clerk_Maxwell#/media/File:James_Clerk_Maxwell.png
Category: '''Fields'''

'''Created by: John Joyce'''

__FORCETOC__

Charging and Discharging a Capacitor

2016-04-18T00:09:09Z

Shisamuddin3:

The main purpose of having a capacitor in a circuit is to store electric charge. For intro physics you can almost think of them as a battery.

CLAIMED BY SAMAH HISAMUDDIN

==The Main Idea==

'''Discharging a Capacitor'''

[[File:Discharging a capacitor wiki.PNG]]

A circuit with a charged capacitor has an electric fringe field inside the wire. This field creates an electron current. The electron current will move opposite the direction of the electric field. However, so long as the electron current is running, the capacitor is being discharged. The electron current is moving negative charges away from the negatively charged plate and towards the positively charged plate. Once the charges even out or are neutralized the electric field will cease to exist. Therefore the current stops running.

In the example where the charged capacitor is connected to a light bulb you can see the electric field is large in the beginning but decreases over time. The electron current is also greater in the beginning and decreases over time. Because of this the light bulb starts out shining brightly but slowly dims and goes out.

'''Charging a Capacitor'''

[[File:Charging a capacitor wiki.PNG]]

Charging a capacitor isn’t much more difficult than discharging and the same principles still apply. The circuit consists of two batteries, a light bulb, and a capacitor. Essentially, the electron current from the batteries will continue to run until the circuit reaches equilibrium (the capacitor is “full”). Just like when discharging, the bulb starts out bright while the electron current is running, but it slowly dims and goes out as the capacitor charges.

The electron current will flow out the negative end of the battery as usual (conventional current will exit the positive end). Positive charges begin to build up on the right plate and negative charges on the left. The electric field slowly decreases until the net electric field is 0. The fringe field is equal and opposite to the electric field caused by everything else.

If you were to draw a box around the capacitor and label it with positive and negative ends it would look like a battery. It also behaves like a battery. The electron current will continue to flow and the electric field will continue to exist until the potential difference across the capacitor is equal to that of the batteries (sum of emf of all batteries in the circuit).

'''Resistors'''

The amount of resistance in the circuit will determine how long it takes a capacitor to charge or discharge. The less resistance (a light bulb with a thicker filament) the faster the capacitor will charge or discharge. The more resistance (a light bulb with a thin filament) the longer it will take the capacitor to charge or discharge. The thicker filament bulb will be brighter, but won't last as long as a thin filament bulb. '''V = IR''', The larger the resistance the smaller the current.

===A Mathematical Model===

'''V = IR'''

'''E = (Q/A)/ε0'''

'''C = Q/V = ε0A/s'''

'''V = (Q/A)s/ε0'''

===A Computational Model===

[[File:Capacitor Charging.svg|Capacitor Charging]]

==Examples==

'''Question 1'''

Doubling the radius of the capacitor

A) quarters the capacitance

B) halves the capacitance

C) doubles the capacitance

D) quadruples the capacitance

Doubling the radius of the capacitor

A) quarters the electric field between the plates

B) halves the electric field between the plates

C) doubles the electric field between the plates

D) quadruples the electric field between the plates

Doubling the distance between the plates

A) quarters the capacitance

B) halves the capacitance

C) doubles the capacitance

D) quadruples the capacitance

Doubling the capacitance

A) quarters the electric field between the plates

B) halves the electric field between the plates

C) doubles the electric field between the plates

D) quadruples the electric field between the plates

ANS: D, B, A, C

'''Question 2'''

[[File:Circuits problem 1 wiki.PNG]]

What is the current at points A,B, and C when the capacitor is not yet charged and when the capacitor is fully charged?

When the capacitor is fully charged what is the charge on the plates?

'''Answer:'''

[[File:Circuits problem 1 wiki answers.PNG]]

'''Question 3'''

[[File:Circuits problem 2 wiki.PNG]]

The switch has been closed for a long time.

What is the current at each point?

What is the charge on the capacitor?

Is the light bulb lit?

The switch is opened.

Immediately after the switch is opened is the bulb lit? After a while?

What current is initially running through the bulb?

Which direction is the current moving?

'''Answer:'''

[[File:Circuits problem 2 wiki answers.PNG]]

==Connectedness==

Capacitor can be temporary batteries. Capacitors in parallel can continue to supply current to the circuit if the battery runs out. This is interesting because the capacitor gets its charge from being connected to a chemical battery, but the capacitor itself supplies voltage without chemicals.

Capacitors are being researched for applications in electromagnetic armour and electromagnetic weapons. Currently capacitors are used as detonators in nuclear weapons. Capacitors also are largely involved in separations of AC and DC components.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
In 1745 Ewald Georg von Kleist was the first to "discover" capacitors in Germany. He connected a generator to glass jars of water and charged them. When he touched the wire they were connected to he shocked himself (discharged the capacitor). At the same time Pieter van Musschenbroek made a similar capacitor and named it the Leyden Jar. When Benjamin Franklin studied the Leyden Jar he determined, among other things, that the charge was stored on the glass. During his studies Franklin was the first to give the capacitor the name battery. Since then batteries have most often been electro-chemical cells of capacitors made of sheets of conducting and dielectric material.

== See also ==
===Further reading===
#Williams, Henry Smith. "A History of Science Volume II, Part VI: The Leyden Jar Discovered"
#Keithley, Joseph F. (1999). The Story of Electrical and Magnetic Measurements: From 500 BC to the 1940s

===External links===

#Wikipedia Page "Capacitor"[https://en.wikipedia.org/wiki/Capacitor]
#Khan Academy[https://www.khanacademy.org/science/physics/circuits-topic]

==References==

#Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions. 3rd ed. Vol. 2. N.p.: John Wiley and Sons, 2002. Print.
#"Capacitor." Wikipedia. Wikimedia Foundation, n.d. Web. 05 Dec. 2015.

[[Category:Which Category did you place this in?]]