Bar Magnet - Revision history

Mjohnson467 at 20:34, 7 October 2020

2020-10-07T20:34:53Z

← Older revision		Revision as of 16:34, 7 October 2020
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	==Main Idea==		==Main Idea==
	~~'''PAGE WIP EDIT BY MOLLIE JOHNSON FALL 2020'''~~
	Permanent magnets are objects made of a material which produces its own persistent magnetic field. A '''bar magnet''' is a type of permanent magnet which is in the shape of a rectangular prism having two '''magnetic poles''', one on either side. In a bar magnet, the [[Magnetic Dipole Moment\|magnetic dipole moment]] vector points from the South pole to the North pole, while the magnitude of the vector depends on the strength of the magnet. The magnetic field of a bar magnet is exactly that of any other dipole, where the lines of magnetic field curl around from the North pole to the South pole. Unlike electric dipoles, the individual magnetic monopoles of a magnetic dipole cannot be separated. If you were to cut a bar magnet in half, you would simply have 2 smaller bar magnets. A magnetic monopole has never been observed.		Permanent magnets are objects made of a material which produces its own persistent magnetic field. A '''bar magnet''' is a type of permanent magnet which is in the shape of a rectangular prism having two '''magnetic poles''', one on either side. In a bar magnet, the [[Magnetic Dipole Moment\|magnetic dipole moment]] vector points from the South pole to the North pole, while the magnitude of the vector depends on the strength of the magnet. The magnetic field of a bar magnet is exactly that of any other dipole, where the lines of magnetic field curl around from the North pole to the South pole. Unlike electric dipoles, the individual magnetic monopoles of a magnetic dipole cannot be separated. If you were to cut a bar magnet in half, you would simply have 2 smaller bar magnets. A magnetic monopole has never been observed.

Mjohnson467 at 20:27, 7 October 2020

2020-10-07T20:27:13Z

← Older revision		Revision as of 16:27, 7 October 2020
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	==Main Idea==		==Main Idea==
			'''PAGE WIP EDIT BY MOLLIE JOHNSON FALL 2020'''
	Permanent magnets are objects made of a material which produces its own persistent magnetic field. A '''bar magnet''' is a type of permanent magnet which is in the shape of a rectangular prism having two '''magnetic poles''', one on either side. In a bar magnet, the [[Magnetic Dipole Moment\|magnetic dipole moment]] vector points from the South pole to the North pole, while the magnitude of the vector depends on the strength of the magnet. The magnetic field of a bar magnet is exactly that of any other dipole, where the lines of magnetic field curl around from the North pole to the South pole. Unlike electric dipoles, the individual magnetic monopoles of a magnetic dipole cannot be separated. If you were to cut a bar magnet in half, you would simply have 2 smaller bar magnets. A magnetic monopole has never been observed.		Permanent magnets are objects made of a material which produces its own persistent magnetic field. A '''bar magnet''' is a type of permanent magnet which is in the shape of a rectangular prism having two '''magnetic poles''', one on either side. In a bar magnet, the [[Magnetic Dipole Moment\|magnetic dipole moment]] vector points from the South pole to the North pole, while the magnitude of the vector depends on the strength of the magnet. The magnetic field of a bar magnet is exactly that of any other dipole, where the lines of magnetic field curl around from the North pole to the South pole. Unlike electric dipoles, the individual magnetic monopoles of a magnetic dipole cannot be separated. If you were to cut a bar magnet in half, you would simply have 2 smaller bar magnets. A magnetic monopole has never been observed.

Laurence12799: /* Examples */

2019-09-02T00:21:17Z

Examples

← Older revision		Revision as of 20:21, 1 September 2019
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	===Middling===		===Middling===
			A bar magnet with a magnetic dipole moment <math>\mu = 0.58 \text{ A} \cdot \text{m}^2</math> lies on the <math>-x</math> axis. A compass is located at the origin. Magnetic North is in the <math>-z</math> direction. Between the bar magnet and the compass is a coil of wire of radius <math>R = 3.5 \text{ cm}</math>. The distance from the center of the coil to the center of the compass is <math>d_{cc} = 9.6 \text{ cm}</math>. The distance from the center of the bar magnet to the center of the compass is <math>d_{bc} = 23.0 \text{ cm}</math>. A steady current of <math>0.96 \text{ A}</math> runs through the coil. The conventional current runs clockwise in the coil when viewed from the location of the compass (the origin). Despite the presence of the magnet and coil, the compass still points north.

			:'''a) Which pole of the bar magnet is closer to the compass?'''

			:'''b) How many turns of wire are in the coil?'''

	===Difficult===		===Difficult===
	We already know that the field of a bar magnet flows out of the North end and into the South end in a curving 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.		We already know that the field of a bar magnet flows out of the North end and into the South end in a curving 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.
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	'''Example 2:'''		'''Example 2:'''

	~~'''(a)''' Which pole of the bar magnet is closer 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 pole''' would have to be nearer the compass.		'''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 pole''' would have to be nearer the compass.

Laurence12799: /* Difficult */

2019-09-02T00:20:02Z

Difficult

← Older revision		Revision as of 20:20, 1 September 2019
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	At a different plane (z ≠ 0), there is no magnetic field, because we can assume that bar magnet acts as a 2-D dipole.		At a different plane (z ≠ 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 A∙m<sup>2</sup> 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.		'''Example 2:'''

	'''(a)''' Which pole of the bar magnet is closer to the compass?		'''(a)''' Which pole of the bar magnet is closer to the compass?

Laurence12799: /* Simple */

2019-09-02T00:02:55Z

Simple

← Older revision		Revision as of 20:02, 1 September 2019
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	A bar magnet is located at the origin of the xy-plane, with its North end aligned with the positive x-axis.		A bar magnet is located at the origin of the xy-plane, with its North end aligned with the positive x-axis.

	:'''a)What are the directions of the magnetic field at the following observation locations?''' ''Above'' the magnet, ''Below'' the magnet, To the ''Left'' of the magnet, To the ''Right'' of the magnet, and In a ''Plane Above'' the magnet <math>(+z)</math>.		:'''a) What are the directions of the magnetic field at the following observation locations?''' ''Above'' the magnet, ''Below'' the magnet, To the ''Left'' of the magnet, To the ''Right'' of the magnet, and In a ''Plane Above'' the magnet <math>(+z)</math>.

	::We know the magnet field of a bar magnet flows from the North Pole to the South Pole in curves.		::We know the magnet field of a bar magnet flows from the North Pole to the South Pole in curves.

Laurence12799: /* Examples */

2019-09-01T23:55:05Z

Examples

@@ Line 76: / Line 76: @@
 ==Examples==
-'''Example 1''': If a bar magnet is located at the origin 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?
+===Simple===
-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.
+:'''a)What are the directions of the magnetic field at the following observation locations?''' ''Above'' the magnet, ''Below'' the magnet, To the ''Left'' of the magnet, To the ''Right'' of the magnet, and In a ''Plane Above'' the magnet <math>(+z)</math>.
 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.

Laurence12799: /* Computational Model */

2019-09-01T23:18:33Z

Computational Model

← Older revision		Revision as of 19:18, 1 September 2019
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	[[File:VFPt cylindrical magnet thumb.svg\|thumb\|left\|The ~~curly~~ magnetic field of a bar magnet]]		[[File:VFPt cylindrical magnet thumb.svg\|thumb\|left\|300px\|The curved 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 of 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 assigned to each end, ~~but~~ it is true that the magnetic field will always flow out of the '~~north~~' end.		As you can see in this picture, the magnetic field of a bar magnet takes the exact same form as the electric field of a dipole. The magnetic field lines flow out of the North pole of the magnet, and into the South pole of the magnet, in a curving fashion. However, the 'poles' are merely just conventions. They do not represent anything, and are terms assigned to each end. However, it is true that the magnetic field will always flow out of the 'North' end.

			Computationally, creating a magnetic dipole is challenging because we cannot use the Law of Superposition to represent it. Instead we must use a ring of current, which produces a dipole field to approximate it. The following code snippet is part of a program which creates a 3D model of a magnetic dipole's field:

	Computationally creating a magnetic dipole is challenging because we cannot use the law of superposition to represent it. Instead we must use a ring of current, which produces a dipole field to approximate it. The following code snippet is part of a program which creates a 3d model of a magnetic dipole field:






	function hh=lforce3d(n,clr)		function hh=lforce3d(n,clr)
	% Lforce3D		% Lforce3D
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	lighting phong;		lighting phong;

	[[File:Dipole_magnetic_field.jpg\|thumb\|center\|The resulting visual is a good representation of a magnetic dipole field]]		[[File:Dipole_magnetic_field.jpg\|thumb\|center\|800px\|The resulting visual is a good representation of a magnetic dipole's field]]

	==Examples==		==Examples==

Laurence12799: /* Mathematical Model */

2019-09-01T23:12:08Z

Mathematical Model

← Older revision		Revision as of 19:12, 1 September 2019
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	:::<math> B = \frac{\mu _{0}}{4\pi } \frac{\mu }{r^{3}}</math>		:::<math> B = \frac{\mu _{0}}{4\pi } \frac{\mu }{r^{3}}</math>


	===Computational Model===		===Computational Model===

Laurence12799: /* Main Idea */

2019-09-01T21:00:49Z

Main Idea

← Older revision		Revision as of 17:00, 1 September 2019
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	:*The primary components of Alnico magnets are aluminum, nickel, cobalt, and iron. These magnets produce a strong magnetic field and retain their magnetic property even under extreme heat.		:*The primary components of Alnico magnets are aluminum, nickel, cobalt, and iron. These magnets produce a strong magnetic field and retain their magnetic property even under extreme heat.
	:2. Neodymium Bar Magnets		:2. Neodymium Bar Magnets
	:*Neodymium bar magnets are made with a mixture of neodymium, boron, and iron. These are both extremely powerful ~~magnets but~~ very brittle.		:*Neodymium bar magnets are made with a mixture of neodymium, boron, and iron. These are both extremely powerful and very brittle magnets.

	~~Neodymium bar magnets are made with a mixture of neodymium, boron, and iron. These are both extremely powerful~~ magnets ~~but very brittle~~.

	Both of these magnets are magnetized by a phenomenon called '''ferromagnetism'''. Unfortunately, ferromagnetism requires quantum mechanics to explain fully, but can be simply explained as the tendency of ferromagnetic materials to align the tiny magnetic dipoles produced by atomic particles, summing to produce a much stronger magnetic dipole moment in the material as a whole.		Both of these magnets are magnetized by a phenomenon called '''ferromagnetism'''. Unfortunately, ferromagnetism requires quantum mechanics to explain fully, but can be simply explained as the tendency of ferromagnetic materials to align the tiny magnetic dipoles produced by atomic particles, summing to produce a much stronger magnetic dipole moment in the material as a whole.
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	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.		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 two different equations. Given a bar magnet with magnetic dipole moment ~~μ, if~~ the observation location is on the same axis as the magnet, assuming that the distance from the observation location to the magnet is much greater than the separation distance of the two poles (r >> s), we find that:		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 two different equations. Given a bar magnet with magnetic dipole moment <math>\mu</math>:
	<math> B = \frac{\mu _{0}}{4\pi }~~\cdot~~ \frac{2\mu }{r^{3}}</math>
			*If the observation location is on the same axis as the magnet, assuming that the distance from the observation location to the magnet is much greater than the separation distance of the two poles <math>(r >> s)</math>, we find that:

			:::<math> B = \frac{\mu _{0}}{4\pi }\frac{2\mu }{r^{3}}</math>

			*If the observation location is on the perpendicular axis of the bar magnet, and assuming that the distance from the observation location to the magnet is much greater than the separation distance of the two poles <math>(r >> s)</math>, we conclude that:

	If the observation location is on the perpendicular axis of the bar magnet, and assuming that the distance from the observation location to the magnet is much greater than the separation distance of the two poles (r >> s), we conclude that:		:::<math> B = \frac{\mu _{0}}{4\pi } \frac{\mu }{r^{3}}</math>
	<math> B = \frac{\mu _{0}}{4\pi }~~\cdot~~ \frac{\mu }{r^{3}}</math>

Laurence12799: /* Main Idea */

2019-09-01T20:48:57Z

Main Idea

← Older revision		Revision as of 16:48, 1 September 2019
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	==Main Idea==		==Main Idea==
	Permanent magnets are objects made of material which produces its own persistent magnetic field. A '''bar magnet''' is a type of permanent magnet which is in the shape of a rectangular prism having two '''magnetic poles''' on either side. In a bar magnet, the [[Magnetic Dipole Moment\|magnetic dipole moment]] vector points from the South pole to the North pole, while the magnitude of the vector depends on the strength of the magnet. The magnetic field of a bar magnet is exactly that of any other dipole, where the lines of magnetic field curl around from the North pole to the South pole. Unlike electric dipoles, the individual magnetic monopoles of a magnetic dipole cannot be separated. If you were to cut a bar magnet in half, you would simply have 2 smaller bar magnets. A magnetic monopole has never been observed.		Permanent magnets are objects made of a material which produces its own persistent magnetic field. A '''bar magnet''' is a type of permanent magnet which is in the shape of a rectangular prism having two '''magnetic poles''', one on either side. In a bar magnet, the [[Magnetic Dipole Moment\|magnetic dipole moment]] vector points from the South pole to the North pole, while the magnitude of the vector depends on the strength of the magnet. The magnetic field of a bar magnet is exactly that of any other dipole, where the lines of magnetic field curl around from the North pole to the South pole. Unlike electric dipoles, the individual magnetic monopoles of a magnetic dipole cannot be separated. If you were to cut a bar magnet in half, you would simply have 2 smaller bar magnets. A magnetic monopole has never been observed.

			A magnetograph can be created by placing a piece of paper over a magnet and sprinkling the paper with iron filings. We can use this to visualize the magnetic field induced by a bar magnet. The particles align themselves with the lines of the magnetic field produced by the magnet. The lines show where the magnetic field exits the material at one pole and re-enters the material at the other pole. It should be noted that the magnetic lines exist in three dimensions, but are only seen in two dimensions in the image.

	A magnetograph can be created by placing a piece of paper over a magnet and sprinkling the paper with iron filings. We can use this to visualize the magnetic field induced by a bar magnet. The particles align themselves with the lines of magnetic force produced by the magnet. The magnetic lines of force show where the magnetic field exits the material at one pole and reenters the material at another pole along the length of the magnet. It should be noted that the magnetic lines of force exist in three dimensions but are only seen in two dimensions in the image.		[[File:Magnetograph1.gif\|center\|400px]]

	[[~~File:Magnetograph1.gif~~]]		The main idea for this topic is to explore the physical properties of bar magnets and how they interact with the environment. The magnetic field produced by a bar magnet, as explained above, is strongest inside the magnet itself. The external location where the field is the strongest is just outside the poles, on axis. A practical way to observe this phenomenon ([[Bar Magnet#A Mathematical Model\|shown mathematically below]]) is using a compass, which being magnetized itself, will point it's North end towards the South pole of any permanent magnet (including the Earth itself! The 'North' pole of the Earth is actually a type S pole), therefore, moving a compass around a bar magnet will accurately illustrate the direction of the net magnetic field vector at any point. Subtracting Earth's magnetic field (varying from 2.5E-5 T to 6.5E-5 T on Earth's surface) will give the direction of the magnetic field of the bar magnet.

	The main idea for this topic is to explore the physical properties of bar magnets and how they interact with the environment. The magnetic field produced by a bar magnet, as explained above, is strongest inside the magnet itself and the external location where the field is the strongest is just outside the poles, on axis. A practical way to observe this phenomenon ([[Bar Magnet#A Mathematical Model\|shown mathematically below]]) is using a compass, which being magnetized itself, will point it'~~s North end towards the South pole of any permanent magnet (including the Earth itself! The~~ '~~North~~' ~~pole~~ of ~~the Earth is actually a type S pole), therefore, moving a compass around a bar magnet will accurately illustrate the direction of the net magnetic field vector at any point. Subtracting Earth~~'~~s magnetic field (varying from 2.5E-5 T to 6.5E-5 T on Earth~~'~~s surface) will give the direction of the magnetic field of the bar magnet.~~		'''There are two different types of Bar Magnets''':

	~~'''Two different types of~~ Bar Magnets~~'''~~		:1. Alnico Bar Magnets
			:*The primary components of Alnico magnets are aluminum, nickel, cobalt, and iron. These magnets produce a strong magnetic field and retain their magnetic property even under extreme heat.
	~~Alnico and Neodymium Bar Magnet~~		:2. Neodymium Bar Magnets
			:*Neodymium bar magnets are made with a mixture of neodymium, boron, and iron. These are both extremely powerful magnets but very brittle.
	The primary components of Alnico magnets are aluminum, nickel, cobalt, and iron. These magnets produce a strong magnetic field and retain their magnetic property even under extreme heat.

	Neodymium bar magnets are made with a mixture of neodymium, boron, and iron. These are both extremely powerful magnets but very brittle.		Neodymium bar magnets are made with a mixture of neodymium, boron, and iron. These are both extremely powerful magnets but very brittle.