# Induced current of a coil surrounding a solenoid

## Homework Statement

A coil with 170 turns, a radius of 5.0 cm, and a resistance of 12 ohms surrounds a solenoid with 230 turns/cm and a radius of 4.7 cm; see the figure. The current in the solenoid changes at a constant rate from 0 to 1.8 A in 0.11 s.

Calculate the magnitude and direction of the induced current in the 170-turn coil.

## Homework Equations

EQ1: induced emf (of a circular conducting loop surrounding a solenoid)
= -(mu_0)(n)(A)(dI/dt)
where n is the turns per length in the solenoid with changing current dI/dt and loop of area A.
EQ2: induced emf = -(dflux/dt)
EQ3: flux = BA
EQ4: B_solenoid = (mu_0)(n)(I)
EQ5: I_induced = (induced emf)/R

## The Attempt at a Solution

I tried to take equation 1 and compute the emf for a single loop, then I multiplied that times 170. I then divided that by 12 to get the current. However, MP says it's wrong. My result was 0.053 A using n = 23,000 turns/m, A = pi * 0.05^2, and dI/dt = 1.8/0.11.

Note: Problem is #67 from Ch 29 of Physics for Scientists and Engineers with Modern Physics By Douglas C. Giancoli, 4th ed.

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