Induced current of a coil surrounding a solenoid

[jchoca]

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.

 

[kuruman]

I got the same number for the current as you. What direction did you give for the current in 12 Ω resistor? Maybe that's what you got wrong.

 

[TSny]

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.

The B field is confined to the solenoid. Instead of the area of the loop, you should use the area of the solenoid.

My result was 0.053 A using ... A = pi * 0.05^2 ...

This is not the correct radius for calculating the area of the solenoid.

 

[kuruman]

This is not the correct radius for calculating the area of the solenoid.

Oops, I missed that even though I looked to make sure that the correct solenoid radius was used.

 

[TSny]

Oops, I missed that even though I looked to make sure that the correct solenoid radius was used.

No problem. We're going to miss things.