Understanding Faraday's Law: Coil in Magnetic Field

[FourierX]

Homework Statement

Actually this is not exactly a homework. I am trying to understand the following situation only.



Consider a ring shaped coil of N turns and area A. Connect it to an external circuit with a twisted pair of leads ( this info is trivial). The resistance of the circuit along with the coil itself is R. Now the coil in a magnetic field.

Suppose the flux through the coil is somehow altered from its initial steady state value (A) to final value (B).

The author claims that the total charge Q that flows through the circuit as a result is independent of the rate of change of the flux. I am having hard time understanding this. Can anyone help me understand it.

Homework Equations

$$\oint$$ E.dl = -d$$\Phi$$/dt

The Attempt at a Solution

faraday's law is the most relevant law here, according to the book. But I am just not getting what the author is saying.

 

[LowlyPion]

I think this lecture covers a lot of what you want to know.
http://ocw.mit.edu/ans7870/8/8.02/videolectures/wl-802-lec16-220k.ram

(Requires Real Player, if that's not a problem for you.)

About 11 minutes in if you are in a rush.

 

[FourierX]

thanks,

i followed the video. It was helpful.

However, i am still not sure about independence of charge with the rate of change of flux. On applying faraday's law

EMF = -Nd$$\Phi$$/dt

In the condition mention in the question above, B is the final M_flux A and the initial M_flux. We are trying to derive Q such that it is independent of d$$\Phi$$/dt.

I am confused with initial and final magentic flux. On just using d$$\Phi$$/dt, here is what i got

I = Nd$$\Phi$$ cos(theta)/dt*(R)

and I = dQ/dt

But still Q is dependent on d$$\Phi$$/dt.

Any clue ?

 

[Defennder]

What is cos theta here? And try equating the expression for I with V/R where V is as given by Faraday's law.

 

[FourierX]

cosine theta is a mistake here. It has to be omitted.

Yeah, i did use Ohm's law there.

But my confusion at this point is, since the final and initial fluxes are given, in Faraday's formula, should emf beemf = -N d(B-A)/dt or just -N d(flux)/dt ?

The final expression is supposed to show that Q is independent of rate of change of flux

 

[Defennder]

It should be $$emf = -\frac{B-A}{\delta t}$$.

 

[FourierX]

did you forget N ?

 

[Defennder]

No I didn't. N was already included in both B and A. Remember that B, A are themselves the flux through the coil. Anyway it should make no difference in the solution.