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## Homework Statement

A long solenoid has a radius of 3 cm, 3000 turn per meter, and carries a current I = IOcos(ωt), where Io is 0.25 A and ω is 628 s−1 . It is placed through a circular loop of wire, radius 5 cm, which has resistance 100 Ω. The magnetic field in a solenoid is B = µonI.

(a) Find the mutual inductance of the solenoid and wire loop.

(b) Find the emf induced in the loop as a function of time, and the peak current which will flow as a result.

(c) Find the maximum electric field induced by the solenoid at the wire loop’s distance from the axis.

## Homework Equations

M = (Nφ) / I

φ = ∫BA

ε = M(dI/dt)

ε = ∫Eds = dφ/dt

## The Attempt at a Solution

I can integrate to find the flux of the solenoid, but I don't have the current of the loop. I can do the opposite and find the flux of the loop since I have the current of the solenoid, but I don't have the magnetic field, I'm stuck on (a)

b) Taking the derivative of I gives Iωsin(ωt), however I don't have the mutual inductance to calculate it

c) Kind of lost on this one