Two nested solenoids and their magnetic fields

[MahalMuh]

Homework Statement:

We have 2 solenoids. The smaller (2) is inside the large one (1) with the axes aligned. Length1 is 0.63, radius1 0.051 m and N1 670 turns. The smaller length2 0.23 m, radius2 0.031 m and N2 260 turns. The larger solenoid has sine form AC with amplitude of I1 1.51 A and frequency1 120 1/s.

a) What is the biggest magnetic field B1 of the larger solenoid?
b) How large is the highest voltage V2 of the smaller solenoid?

Relevant Equations:

B1 = u0*N1*I1 / length1
Several forms for M, inductance
I = I0 * sin(frequency*t)
Faradays's law for V =

a) is pretty clear and got correct but b) I'm struggling with.

For b) I guess one could take the derivative of I and specify the moment t when you can plug that into Faraday's law. Or could this be solved somehow with inductance?

 

[BvU]

Hi,

You didn't write down Faraday's law, but that is indeed what you need.

Faraday's law needs $\displaystyle{d(BA)\over dt}$ and you have all you need to calculate the generated emf, which then comes out as a function of time.

(I am fairly certain you are allowed to use B1 as if it's constant over the length of the small coil).