Magnetism - Revision history

Rice at 03:28, 5 March 2024

2024-03-05T03:28:55Z

← Older revision		Revision as of 03:28, 5 March 2024
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	The general proof of Ampere's Law involves starting from Biot-Savart Law, integrating to a term and a Maxwell's term. I will do the proof later.		The general proof of Ampere's Law involves starting from Biot-Savart Law, integrating to a term and a Maxwell's term. I will do the proof later.

			[[Category:Physics]]

Rice: /* Rings */

2024-03-04T21:27:22Z

Rings

← Older revision		Revision as of 21:27, 4 March 2024
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	The general proof of Ampere's Law involves starting from Biot-Savart Law, integrating to a term and a Maxwell's term. I will do the proof later.		The general proof of Ampere's Law involves starting from Biot-Savart Law, integrating to a term and a Maxwell's term. I will do the proof later.

	~~= Uniform Magnetic Field =~~

	~~A pair of current loops can create a very uniform magnetic field in the middle.~~

Rice: /* Special Field: Wire */

2024-03-04T21:26:08Z

Special Field: Wire

← Older revision		Revision as of 21:26, 4 March 2024
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	A '''moving charge''' causes a magnetic field, following the right hand		A '''moving charge''' causes a magnetic field, following the right hand
	rule: Your thumb pointing towards the direction of movement of the		rule: Your thumb pointing towards the direction of movement of the positive charge, and your other fingers wrap around to indicate the direction of the magnetic field.
	positive charge, and your other fingers wrap around to indicate the
	direction of the magnetic field.

	A circulating current forms a magnetic dipole.		A circulating current forms a magnetic dipole.
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	</math> is distance from the wire.		</math> is distance from the wire.

	Any component going along the direction of current is cancelled by cross		Any component going along the direction of current is cancelled by cross product. '''Something else'''. Therefore, it is unsurprising that magnetic field is circulating.
	product. '''Something else'''. Therefore, it is unsurprising that
	magnetic field is circulating.

	== ~~Special Field: Wire~~ ==		== Straight Line ==

	~~- TODO: Later fill out~~ <~~01-03-24, xydxydxyd1~~> -		Consider a straight line segment starting at <math>z_1</math>and stopping at <math>z_2</math>

	=~~= Loops ==~~		<math>\vec{B} = \frac{\mu_0 I }{4 \pi \rho} \left( \frac{z_2}{\sqrt{z_2^2 + \rho^2} } - \frac{z_1}{\sqrt{z_1^2 + \rho^2} } \right) \hat{e_\phi}</math>

	Let there be a loop of current flowing clockwise. The magnetic field		== Circular Loops ==
	inside the loop is always going out of the page, whereas the field
	outside always go into the page.		Let there be a loop of current flowing clockwise. The magnetic field inside the loop is always going out of the page, whereas the field outside always go into the page.

	This can be proven by considering each single length of wire. The shape		This can be proven by considering each single length of wire. The shape
	of the loop does not matter.		of the loop does not matter.

			A pair of circular loops can produce a very uniform magnetic field in the middle.

			=== Solenoid ===
			'''Solenoids''' use this property to create uniform magnetic fields. They are essentially a long coil of current. Inside the solenoid there is a strong, uniform magnetic field. At the ends, the strength drop drastically.

			The field created can be derived from adding together circular loops.

			<math>
			\vec{B}_{inside, axis} = \mu_0 \frac{N}{L} I \hat{k}
			</math>

			=== Toroidal Solenoid ===
			What if we wrap around the solenoid so that they form a loop of coil? we get a circulating magnetic field. The magnitude is the same.

			== Rings ==
			Consider a hollow inner conducting shell inside a hollow outer conducting shell. Run current through the shells and you get a ring of magnetic field.

	= Ampere's Law of Magnetic field =		= Ampere's Law of Magnetic field =
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	</math>		</math>

	The general proof of Ampere's Law involves starting from Biot-Savart		The general proof of Ampere's Law involves starting from Biot-Savart Law, integrating to a term and a Maxwell's term. I will do the proof later.
	Law, integrating to a term and a Maxwell's term. I will do the proof
	later.

	= Uniform Magnetic Field =		= Uniform Magnetic Field =

	A pair of current loops can create a very uniform magnetic field in the		A pair of current loops can create a very uniform magnetic field in the middle.
	middle.

	~~= Solenoid =~~

	~~Solenoid is a very useful way to create magnetic fields. They are~~
	~~essentially a long coil of current. Inside the solenoid there is a~~
	~~strong, uniform magnetic field. At the ends, the strength drop~~
	~~drastically.~~

	~~The field created can be derived from adding together circular loops.~~

	~~<math>~~
	~~\vec{B}_{inside, axis} = \mu_0 \frac{N}{L} I \hat{k}~~
	~~</math>~~

Rice at 21:50, 1 March 2024

2024-03-01T21:50:54Z

@@ Line 39: / Line 39: @@
 <math>
 \oint_C \vec{B} \cdot d \vec{l} = \mu_0 \iint_{S_L} \vec{J} \cdot d
-\vec{s} = \mu_0 i
+\vec{s} = \mu_0 I
 </math>
@@ Line 45: / Line 45: @@
 Law, integrating to a term and a Maxwell's term. I will do the proof
 later.

Rice at 21:32, 1 March 2024

2024-03-01T21:32:42Z

← Older revision		Revision as of 21:32, 1 March 2024
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	= Ampere's Law of Magnetic field =		= Ampere's Law of Magnetic field =

	~~<math>~~
	~~\oint_C \vec{B} \cdot d \vec{l} = \oint_C \left( \frac{\mu_0 I}{2 \pi~~
	~~\rho} \cdot d \vec{l} \right) = \mu_0 I~~
	~~</math>~~

	<math>		<math>
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	</math>		</math>

	~~Consider a very long wire, with curve C around the wire. There is~~		The general proof of Ampere's Law involves starting from Biot-Savart
			Law, integrating to a term and a Maxwell's term. I will do the proof
	~~<math>~~		later.
	~~d \vec{l} = dz \hat{k} + d \rho \hat{\rho} + \rho d \phi \hat{e_\phi}~~
	~~</math>~~

	~~where <math>\hat{k}</math> is the direction~~ of ~~the wire,~~
	~~<math>\hat{\rho}</math> is the direction away from the wire~~, and
	~~<math>\hat{e_\phi}</math> is the direction tangential to the wire~~.

Rice at 21:27, 1 March 2024

2024-03-01T21:27:01Z

← Older revision		Revision as of 21:27, 1 March 2024
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	<math>		<math>
	d \vec{l} = dz \hat{k} + d \rho \hat{\rho} + \rho d \phi \hat{e_\phi}		d \vec{l} = dz \hat{k} + d \rho \hat{\rho} + \rho d \phi \hat{e_\phi}
	</math>		</math>

Rice at 21:26, 1 March 2024

2024-03-01T21:26:08Z

← Older revision		Revision as of 21:26, 1 March 2024
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	\vec{s} = \mu_0 i		\vec{s} = \mu_0 i
	</math>		</math>

			Consider a very long wire, with curve C around the wire. There is

			<math>
			d \vec{l} = dz \hat{k} + d \rho \hat{\rho} + \rho d \phi \hat{e_\phi}
			</math>

			where <math>\hat{k}</math> is the direction of the wire,
			<math>\hat{\rho}</math> is the direction away from the wire, and
			<math>\hat{e_\phi}</math> is the direction tangential to the wire.

Rice at 21:22, 1 March 2024

2024-03-01T21:22:01Z

@@ Line 23: / Line 23: @@
 == Special Field: Wire ==
 == Loops ==
@@ Line 31: / Line 33: @@
 This can be proven by considering each single length of wire. The shape
-of the loop does not matter
+of the loop does not matter.

Rice at 21:17, 1 March 2024

2024-03-01T21:17:05Z

← Older revision		Revision as of 21:17, 1 March 2024
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	magnetic field is circulating.		magnetic field is circulating.

	== Special Field ~~--- Infinitely Long~~ Wire ==		== Special Field: Wire ==

			== Loops ==

			Let there be a loop of current flowing clockwise. The magnetic field
			inside the loop is always going out of the page, whereas the field
			outside always go into the page.

			This can be proven by considering each single length of wire. The shape
			of the loop does not matter

Rice at 21:58, 29 February 2024

2024-02-29T21:58:26Z

← Older revision		Revision as of 21:58, 29 February 2024
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	== Calculate Field ==		== Calculate Field ==
			[[File:CurrentMagneticField.png\|thumb\|Magnetic field of a current with right hand rule]]<math>
	<math>
	\vec{B} (\vec{r})		\vec{B} (\vec{r})
	= \frac{ \mu_0 }{ 4 \pi } \frac{ I_1 d\vec{l}_1 \times \hat{r}}{ r^2 }		= \frac{ \mu_0 }{ 4 \pi } \frac{ I_1 d\vec{l}_1 \times \hat{r}}{ r^2 }
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	Where <math> \mu_0 </math> is magnetic permeability, and <math> \rho		Where <math> \mu_0 </math> is magnetic permeability, and <math> \rho
	</math> is distance from the wire.		</math> is distance from the wire.
	~~[[File:CurrentMagneticField.png\|thumb\|Magnetic field of a current with right hand rule]]~~
	Any component going along the direction of current is cancelled by cross		Any component going along the direction of current is cancelled by cross
	product. '''Something else'''. Therefore, it is unsurprising that		product. '''Something else'''. Therefore, it is unsurprising that