Professor K brings a 75-turn coil of radius 35mm into class for a demonstration of Faraday's Law. He applies a spatially uniform magnetic field parallel to the axis of the coil with a magnet. By moving the magnet closer to the coil, he increases the magnitude of the field at a constant rate from 18mT to 43mT in 240ms. The coil has a resistance of 15milli Ohms (this piece of information is for two more parts which I know how to obtain easily).
Using Faraday's Law, derive a formula for the induced emf in the coil and use it to calculate the numerical value of the induce emf.
ε = NΔΦ/Δt (while this is not the general form, it's the form which will apply here since the concern is with magnitude.)
Φ = BA
The Attempt at a Solution
First I drew my diagram. I drew the coil as basically a cylinder. I drew the magnetic field parallel to the cylinder (so it would be going up) while the induced current would be in the opposite direction (down). This could very well be my mistake, but I'm not sure.
I'm thinking using the values of B = 43mT and B = 18mT, find ΔΦ = A(43mT-18mT) = A25mT.
Δt is obviously 0.240s. However I don't know what A should be in this problem.
If A is pi*r^2, the answer does not come out correct.
The answer is ε = 0.0301 volts. Is this an error on my end or the professor's? This is an answer for a practice exam for the final exam.