# Calculating the magnetic field inside a field coil

1. Feb 25, 2013

### newageanubis

1. The problem statement, all variables and given/known data
(This is a bonus question for a lab I have coming up next week.)

In this part of the lab, a large field coil is hooked up to a function generator that outputs a 100 kHz, 10V peak-to-peak waveform. A smaller test coil is connected to an oscilloscope and slowly inserted into the field coil. The induced emf can be read off of the oscilloscope. Knowing the number of turns and cross-sectional area of the test coil, calculate the magnetic field B inside the large test coil.

2. Relevant equations
ε = -L*(dI/dt)
B = μNI/L

3. The attempt at a solution
Solution 1:
I'm thinking that the emf in the test coil can be read off of the oscilloscope and represented as a sinusoidal function. The inductance of the test coil can be determined from its known geometric properties. Then, you rearrange the equation so that it reads:

-ε/L dt = dI

And integrate, taking I = 0 at t = 0 as the initial value. Then, since B = μNI/L, the magnetic field inside the field coil can be found as a function of time. You solve for the time of interest (time at which you want to know the B field) using the ε function and a specific ε value at the time of interest, and then solve for the B field using the previously determined function.

The only problem (other than the fact that I'm probably wrong) is that this solution requires me to have access to the dimensions of the field coil, which I don't know if I will.

2. Feb 25, 2013

### newageanubis

Anyone? :(

3. Feb 26, 2013

### rude man

I think you're on the wrong track.

Test coil: how about Newton's emf = -Nd(phi)/dt?
What is phi in terms of area of the coil and the (average) value of the B field inside that area?

4. Feb 26, 2013

### newageanubis

$\Phi$ = B_avg * A for this situation, I believe. The test coil isn't moved once it is inside the field coil, so the effective area doesn't change.

5. Feb 26, 2013

### rude man

Ah, true.

But B does change. 100 KHz ... and emf = d(phi)/dt, not phi. So what is d(phi)/dt? Does that give you dB/dt?

And if you know dB/dt which will be a sinusoid, can you from that deduce the time-varying B field itself?