# Induced current in a coil around a solenoid

**1. The problem statement, all variables and given/known data**

A coil with 150 turns, a radius of 5.0 cm, and a resistance of 12 Ω surrounds a solenoid with 300 turns/cm and a radius of 4.3cm; see the figure. The current in the solenoid changes at a constant rate from 0 to 1.8 A in 0.12 s.

**2. Relevant equations**

B from solenoid = μ*n*I(t)

Induced emf = d(BA)/dt

**3. The attempt at a solution**

First I found the magnetic field generated by the solenoid as a function of time:

B(t) = (1.8/.12)*μ*n*t

Then found induced emf in the coil using d(B[itex]_{solenoid}[/itex]*A[itex]_{coil}[/itex])/d(t)

Then divided that result by the coil’s resistance to get induced current, which I found to be .000093 A. However, this is wrong and I’m not sure where I’m making a mistake.

Thanks

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