Inductance - Revision history

Bcosta6: /* Further reading */

2016-04-18T03:12:08Z

Bcosta6: /* Difficult */

2016-04-18T03:10:48Z

Difficult

← Older revision		Revision as of 23:10, 17 April 2016
Line 64:		Line 64:

	What is the self-inductance of a solenoid that has 100 loops, a radius of 5 cm, and is 1 meter long.		What is the self-inductance of a solenoid that has 100 loops, a radius of 5 cm, and is 1 meter long.

			Now that we have derived the general formulas for inductance, we can solve this problem in the following manner,

	[[File:Diffinductance.png]]		[[File:Diffinductance.png]]

Bcosta6: /* Middling */

2016-04-18T03:09:38Z

Middling

← Older revision		Revision as of 23:09, 17 April 2016
Line 53:		Line 53:
	As stated, the Non Coulomb electric field polarizes the solenoid.		As stated, the Non Coulomb electric field polarizes the solenoid.

	Given the polarization of the solenoid a new Electric field is created		Given the polarization of the solenoid a new Electric field is created as seen in the above picture in yellow.

			Therefore, the change in voltage of the solenoid is equal to the induced emf, that we just derived in previous steps and is named as equation (1). Assuming there is no resistance in the solenoid coil, the change in voltage for the solenoid equals the emf induced.

			As you can see in equation (2) from the picture above, the term "L" is the inductance of the device, the inductor, in this case the solenoid.

			Comparing equations (1) and (2) we derive the general formula for Inductance

	===Difficult===		===Difficult===

Bcosta6: /* Middling */

2016-04-18T03:03:47Z

Middling

← Older revision		Revision as of 23:03, 17 April 2016
Line 44:		Line 44:
	[[File:Equationinductance.png]]		[[File:Equationinductance.png]]

	~~-The self inductance~~ is the ~~constant~~ in the ~~inductance formula solved above~~. ~~This means that~~ the ~~self inductance constant for~~ a solenoid is (~~μ0N/d(piR^2~~)		Given a circuit consisting of a solenoid, a resistor and a emf, in which a current is changing, increasing in this example.

			Recall that when there is a change in the magnetic flux, there is a emf produced. In this example, the generated emf due to the change in the magnetic flux generated by the change in the current, is what we will call the emf induced, since it is induced by the changing current in the solenoid.

			To understand what is happening in the solenoid in a qualitative matter, lets take a look at the solenoid when there is a changing current.

			As the current increases, the magnetic field generated by the solenoid increases. There is a Non Coulomb electric field generated by the changing magnetic field opposing the direction of the increasing magnetic field. In the picture, the Non Coulomb electric field (Enc) is in red.
			As stated, the Non Coulomb electric field polarizes the solenoid.

			Given the polarization of the solenoid a new Electric field is created

	===Difficult===		===Difficult===

Bcosta6: /* Simple */

2016-04-18T02:55:55Z

Simple

← Older revision		Revision as of 22:55, 17 April 2016
Line 35:		Line 35:

	[[File:Inductance - 4.png]]		[[File:Inductance - 4.png]]

	~~B=μ0NI/d~~
	~~emf = \|d(mag flux)/dt\| = d/dt\|μ0NI/d(piR^2)\| = μ0NI/d(piR^2)dI/dt~~
	~~emf = N(μ0N/d(piR^2)dI/dt)= (μ0N^2/d(piR^2)dI/dt)~~

	===Middling===		===Middling===

Bcosta6: /* Difficult */

2016-04-18T02:54:39Z

Difficult

← Older revision		Revision as of 22:54, 17 April 2016
Line 54:		Line 54:
	What is the self-inductance of a solenoid that has 100 loops, a radius of 5 cm, and is 1 meter long.		What is the self-inductance of a solenoid that has 100 loops, a radius of 5 cm, and is 1 meter long.

	~~- the self inductance would be (μ0100/1(pi~~.~~01^2)= 3.95e-8 henries~~		[[File:Diffinductance.png]]

	==Connectedness==		==Connectedness==

Bcosta6: /* Middling */

2016-04-18T02:46:21Z

Middling

← Older revision		Revision as of 22:46, 17 April 2016
Line 45:		Line 45:

	[[File:Noncoulumb.png]]		[[File:Noncoulumb.png]]

			[[File:Equationinductance.png]]

	-The self inductance is the constant in the inductance formula solved above. This means that the self inductance constant for a solenoid is (μ0N/d(piR^2)		-The self inductance is the constant in the inductance formula solved above. This means that the self inductance constant for a solenoid is (μ0N/d(piR^2)

Bcosta6: /* A Computational Model */

2016-04-18T02:20:17Z

A Computational Model

← Older revision		Revision as of 22:20, 17 April 2016
Line 23:		Line 23:

	Here is a visual display of the magnetic field in a solenoid [[File:Inductance - 2.png]]		Here is a visual display of the magnetic field in a solenoid [[File:Inductance - 2.png]]

			To understand the inductance lets go step by step through the examples and get the main formula for Inductance.

	==Examples==		==Examples==

Bcosta6: /* A Computational Model */

2016-04-18T02:18:56Z

A Computational Model

← Older revision		Revision as of 22:18, 17 April 2016
Line 22:		Line 22:
	===A Computational Model===		===A Computational Model===

	Here is a visual display of ~~inductance~~ in a solenoid [[File:Inductance - 2.png]]		Here is a visual display of the magnetic field in a solenoid [[File:Inductance - 2.png]]

	==Examples==		==Examples==

Bcosta6: /* The Main Idea */

2016-04-18T02:17:01Z

The Main Idea

← Older revision		Revision as of 22:17, 17 April 2016
Line 8:		Line 8:
	According to this law there is an induced electromotive force in any circuit whenever the magnetic flux linked with that circuit changes. A circuit carrying a current always has some linked magnetic flux due to that current. A change in the current leads to a change in the flux, and the change in flux in turn gives rise to an induced e.m.f. Furthermore, the induced e.m.f. is always in such a direction that it tends to oppose the change in current: there is a forward e.m.f. if the current is being reduced and a backward e.m.f.		According to this law there is an induced electromotive force in any circuit whenever the magnetic flux linked with that circuit changes. A circuit carrying a current always has some linked magnetic flux due to that current. A change in the current leads to a change in the flux, and the change in flux in turn gives rise to an induced e.m.f. Furthermore, the induced e.m.f. is always in such a direction that it tends to oppose the change in current: there is a forward e.m.f. if the current is being reduced and a backward e.m.f.
	if it is being increased.		if it is being increased.

			[[File:Inductance - 3.png]]

			As seen in figure (A) the induced emf, due to a solenoid, in this case is in such a direction that opposes the change in current. In this case the induced emf acts like a battery placed backwards in comparison of the original one. This, reduces the rate at which the current is increasing.

			The opposite happens in figure (B) the induced emf, due to a solenoid in this case, is in such direction that opposes the change in current. In this case the emf acts like a battery placed in the same direction as the original one. This, reduces the rate at which the current decreases.

	===A Mathematical Model===		===A Mathematical Model===

← Older revision		Revision as of 23:12, 17 April 2016
Line 83:		Line 83:

	Information for this page was found in Matter and Interactions Volume II. If you would like to know more about this topic or other topics like it, please reference this book.		Information for this page was found in Matter and Interactions Volume II. If you would like to know more about this topic or other topics like it, please reference this book.

			===Images===

			All images are property of one of the collaborators.

	==References==		==References==