MagneticFields - Revision history

Patapom at 16:52, 11 February 2010

2010-02-11T16:52:28Z

Patapom at 16:46, 11 February 2010

2010-02-11T16:46:14Z

Patapom at 16:45, 11 February 2010

2010-02-11T16:45:29Z

Patapom at 16:14, 11 February 2010

2010-02-11T16:14:03Z

Patapom at 16:10, 11 February 2010

2010-02-11T16:10:04Z

Patapom at 15:50, 11 February 2010

2010-02-11T15:50:23Z

Patapom at 15:43, 11 February 2010

2010-02-11T15:43:13Z

Patapom at 15:35, 11 February 2010

2010-02-11T15:35:37Z

Patapom at 15:25, 11 February 2010

2010-02-11T15:25:43Z

Patapom at 15:18, 11 February 2010

2010-02-11T15:18:15Z

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 For a special project of mine that will certainly revolution the entire world [[File:S2.gif]], I needed to understand basic Electro-Magnetism theory.
-This page deals with my encounter and difficulties but also with the results of my research.
+This page and the next deal with my encounters and difficulties but also with the results of my research.
 == Electro-Magnetism ==

← Older revision		Revision as of 16:46, 11 February 2010
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	I borrowed the book and after careful reading, I saw it explained everything about Vizimag and even contained the "source code" of the most important parts.		I borrowed the book and after careful reading, I saw it explained everything about Vizimag and even contained the "source code" of the most important parts.

		+
		+	== What's Next Then ? ==
	Let's see where it led me in [[MagneticFields2\|Magnetic Fields (Part 2)]]		Let's see where it led me in [[MagneticFields2\|Magnetic Fields (Part 2)]]

@@ Line 86: / Line 86: @@
 Materials susceptible to magnetism see their <math>\mathbf{M}</math> magnetic moment <u>induced</u> by any external field they are set into. This external field can be generated by permanent magnets, electro-magnets (solenoid coils) or even other magnetized materials (since permanent magnets are, after all, strongly magnetized materials themselves).
-The figure below shows the process of induced magnetism by an external field, something we all could experienced as a kid when playing with magnets :
+The figure below shows the process of induced magnetism by an external field, something we all could experience as a kid when playing with magnets :
 [[File:Inducedmagnetism.jpg]]
@@ Line 105: / Line 105: @@
 <math>\mathbf{H}</math> and <math>\mathbf{M}</math> are both discontinuous fields as <math>\mathbf{H}</math> can be decomposed as the external and internal fields <math>\mathbf{H_e}</math> and <math>\mathbf{H_i}</math> and <math>\mathbf{M}</math> exists only <u>inside</u> a magnetic material and is <math>\mathbf{0}</math> outside.
-Note that the internal field <math>\mathbf{H_i}</math> is produced by the induced internal field <math>\mathbf{M}</math> and is called the ''demagnetizing field'' that is defined as <math>\mathbf{H_i}=k\mathbf{M}</math> where <math>k</math> is a factor that is uniquely defined by the geometry of the piece of material (e.g. it's <math>-1/3</math> for a sphere).
+Note that the internal field <math>\mathbf{H_i}</math> is produced by the induced internal field <math>\mathbf{M}</math> and is called the ''demagnetizing field'' that is defined as <math>\mathbf{H_i}=k\mathbf{M}</math> where <math>k</math> is the ''demagnetizing factor'' and is uniquely defined by the geometry of the piece of material (e.g. it's <math>-1/3</math> for a sphere).
@@ Line 119: / Line 119: @@
 == In Practice ==

@@ Line 97: / Line 97: @@
 The figure below shows a representation of the 3 types of materials and their induced internal field <math>\mathbf{M}</math> (or <math>\mathbf{J}</math> here) :
-[[File:Susceptibilities.jpg]]
+[[File:Susceptibilities.jpg|600px]]
 === Merging Vectors ===
-We saw 3 different vectors <math>\mathbf{B}</math>, <math>\mathbf{H}</math> and <math>\mathbf{M}</math>.
+We saw 3 different types of vectors : <math>\mathbf{B}</math>, <math>\mathbf{H}</math> and <math>\mathbf{M}</math>.
 <math>\mathbf{H}</math> and <math>\mathbf{M}</math> are both discontinuous fields as <math>\mathbf{H}</math> can be decomposed as the external and internal fields <math>\mathbf{H_e}</math> and <math>\mathbf{H_i}</math> and <math>\mathbf{M}</math> exists only <u>inside</u> a magnetic material and is <math>\mathbf{0}</math> outside.
@@ Line 113: / Line 113: @@
 And outside a material we have :
 <math>\mathbf{B_e}=\mu_0\mathbf{H_e}</math>
 == In Practice ==

@@ Line 95: / Line 95: @@
 * '''Ferromagnetic''' materials, which have a very high (e.g. <math>10^{3}</math>) and positive susceptibility (thus generating a very high <math>\mathbf{M}</math> in the same direction as <math>\mathbf{H}</math>)
-The figure below shows a representation of the 3 types of materials and their induced internal field <math>\mathbf{M}</math> and <math>\mathbf{H_i}</math> :
+The figure below shows a representation of the 3 types of materials and their induced internal field <math>\mathbf{M}</math> (or <math>\mathbf{J}</math> here) :
-Note how the induced internal field <math>\mathbf{M}</math> also produces an internal field <math>\mathbf{H_i}</math>.
+[[File:Susceptibilities.jpg]]
@@ Line 105: / Line 104: @@
 <math>\mathbf{H}</math> and <math>\mathbf{M}</math> are both discontinuous fields as <math>\mathbf{H}</math> can be decomposed as the external and internal fields <math>\mathbf{H_e}</math> and <math>\mathbf{H_i}</math> and <math>\mathbf{M}</math> exists only <u>inside</u> a magnetic material and is <math>\mathbf{0}</math> outside.
 So in general, inside a material we have :

@@ Line 90: / Line 90: @@
 [[File:Inducedmagnetism.jpg]]
-The "magnetizability" of a material is called its magnetic ''susceptibility'' and written as <math>\chi</math> and we can write <math>\mathbf{M}=\chi\mathbf{H}</math> that shows how the "internal magnetization" <math>\mathbf{M}</math> is induced by the external field <math>\mathbf{H}</math> via the <math>\chi</math> factor. There are 3 classes of susceptible materials :
+The "magnetizability" of a material is called its magnetic ''susceptibility'' <math>\chi</math> and we can write <math>\mathbf{M}=\chi\mathbf{H}</math> that shows how the "internal magnetization" <math>\mathbf{M}</math> is induced by the external field <math>\mathbf{H}</math> via the <math>\chi</math> factor. There are 3 classes of susceptible materials :
 * '''Paramagnetic''' materials, which have a very low (e.g. <math>10^{-4}</math>) and positive susceptibility (thus generating a very low <math>\mathbf{M}</math> in the same direction as <math>\mathbf{H}</math>)
 * '''Diamagnetic''' materials, which have a very low (e.g. <math>-10^{-4}</math>) and negative susceptibility (thus generating a very low <math>\mathbf{M}</math> in the opposite direction as <math>\mathbf{H}</math>)
 * '''Ferromagnetic''' materials, which have a very high (e.g. <math>10^{3}</math>) and positive susceptibility (thus generating a very high <math>\mathbf{M}</math> in the same direction as <math>\mathbf{H}</math>)
 == In Practice ==

← Older revision		Revision as of 15:43, 11 February 2010
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	[[File:Inducedmagnetism.jpg]]		[[File:Inducedmagnetism.jpg]]
		+
		+	The "magnetizability" of a material is called its magnetic ''susceptibility'' and written as <math>\chi</math> and we can write <math>\mathbf{M}=\chi\mathbf{H}</math> that shows how the "internal magnetization" <math>\mathbf{M}</math> is induced by the external field <math>\mathbf{H}</math> via the <math>\chi</math> factor. There are 3 classes of susceptible materials :
		+	* '''Paramagnetic''' materials, which have a very low (e.g. <math>10^{-4}</math>) and positive susceptibility (thus generating a very low <math>\mathbf{M}</math> in the same direction as <math>\mathbf{H}</math>)
		+	* '''Diamagnetic''' materials, which have a very low (e.g. <math>-10^{-4}</math>) and negative susceptibility (thus generating a very low <math>\mathbf{M}</math> in the opposite direction as <math>\mathbf{H}</math>)
		+	* '''Ferromagnetic''' materials, which have a very high (e.g. <math>10^{3}</math>) and positive susceptibility (thus generating a very high <math>\mathbf{M}</math> in the same direction as <math>\mathbf{H}</math>)


	== In Practice ==		== In Practice ==

@@ Line 54: / Line 54: @@
-== In Practice ==
+== Two Cases to Distinguish ==
 As always, physics manuals are great if you already understand what the guy is talking about. Also, they always use the examples of solenoids with a current and a given number of coils whereas, although I knew electric current and magnetic fields are always strongly related, I needed a book that took me to the origins : permanent magnets.
@@ Line 77: / Line 77: @@
 === Permanent Magnets ===
-You can see permanent magnets as a more or less uniform assembly of atomic dipoles. An atomic dipole can be thought as an electron orbiting about its atomic structure and creating a small current loop responsible for a tiny magnetic moment as shown on the figure below :
+You can see permanent magnets as a more or less uniform assembly of atomic dipoles, each dipole carrying a small magnetic moment <math>d\mathbf{M}</math> that is responsible for rotating the dipole in the axis of any external field. An atomic dipole can be naively thought of as an electron orbiting about its atomic structure and creating a small current loop responsible for a tiny magnetic moment <math>d\mathbf{M}</math> as shown on the figure below :
 [[File:Barmagnetshowingelectronspins.jpg]]
-The small current loops sort of cancel out each other inside the material only to leave surface dipoles which are the most active at the north and south poles of the magnets. These 2 oriented poles are resulting from the statistic sum of the orientation of the microscopic dipoles, finally yielding the global macroscopic dipole moment <math>\mathbf{M}</math>.
+The small current loops sort of cancel out each other inside the material only to leave surface dipoles which are the most active at the north and south poles of the magnets. These 2 oriented poles are resulting from the statistic sum of the orientation of each microscopic dipoles, finally yielding the global macroscopic dipole moment <math>\mathbf{M}</math>.
+The figure below shows the process of induced magnetism by an external field, something we all could experienced as a kid when playing with magnets :

@@ Line 73: / Line 73: @@
 Indeed, you can distinguish 2 cases:
-# Permanent Magnets, where <math>\mathbf{M}</math> is actually "generated" from the magnet as the statistic macroscopic sum of all the small microscopic dipoles <math>\mathbf{dM}</math>
+# Permanent Magnets, where <math>\mathbf{M}</math> is actually "generated" from the magnet as the statistic macroscopic sum of all the small microscopic dipoles <math>d\mathbf{M}</math>
 # Magnetic Materials, where <math>\mathbf{M}</math> is actually <u>induced</u> by the external magnetic field in which the material is set. In that case, <math>\mathbf{M}</math> is then a factor of <math>\mathbf{H}</math>, the external field, but also generates itself a new <math>\mathbf{H'}</math> coming from its own magnetization.
+_

@@ Line 14: / Line 14: @@
 ::: <math>\nabla \times \mathbf{H} = \mathbf{j}</math>
+|
-:: (1)
+::: (1)
 |-
+|
 ::: <math>\nabla \cdot \mathbf{B} = 0</math>
+|
-:: (2)
+::: (2)
 |-
+|
 ::: <math>\nabla \times \mathbf{E} = \mathbf{0}</math>
+|
-:: (3)
+::: (3)
 |-
+|
 ::: <math>\nabla \cdot \mathbf{D} = \rho_e</math>
+|
-:: (4)
+::: (4)
 |}
@@ Line 63: / Line 63: @@
 {|
+|
-::: <math>\mathbf{B}=\mu_0(\mathbf{H} + \mathbf{M}</math>
+::: <math>\mathbf{B}=\mu_0(\mathbf{H} + \mathbf{M})</math>
+|
 ::: (5)
 |}
+_