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.
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