Calculating Induced Current in a Coil Surrounding a Changing Current Solenoid

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Homework Statement

A coil with 140 turns, a radius of 5.2 cm, and a resistance of 11.0 Ω surrounds a solenoid with 200 turns/cm and a radius of 4.5 cm. The current in the solenoid changes at a constant rate from 0 A to 2.0 A in 0.10 s. Calculate the magnitude and direction of the induced current in the 140-coil.

Homework Equations

EMF = -N (dφ/dt)

The Attempt at a Solution

I_ind = EMF/ R of the coil, due to Ohm's law.

So I know that I should find the EMF of the coil using
EMF = -N (dφ/dt) = -N (A) (dB/ dt)

I should find dB/dt, but I'm not totally sure how. I think I could use the magnetic field formula for a ring at the center maybe B= (μ₀I) / (2 r_coil) , where the current, I , is changing due to the solenoid?

 

[Delta2]

I know many will find this a stupid question but is the coil with the 140 turns forming a close loop between its two ends? Can you provide some sort of schematic to let us see how exactly the two coils are.
Anyway if the coils configuration is as I think it is, then you should indeed try to find dB/dt (have in mind that as area A you should take the area of the solenoid(the coil with the 200turns/cm) not the area of the coil with the radius of 5.2cm). I believe you should use the formula $B=\mu_0I\frac{n}{L}$ where $\frac{n}{L}=200$ .

 

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Yes, I forgot to post the picture.

 

[ooohffff]

Great I got the answer (see below). Could you clarify though, why I would use the area of the solenoid versus the single coil?

B_solenoid = μ₀ I (N/L)
dB/dt = μ₀(dI/dt)(N/L)
EMF = N_coil (dB/dt) A_solenoid = N_coil [μ₀(dI/dt)(N/L) ] A _solenoid = .44768V
I_ind = .44768V/ 11Ω = .04069A

 

[Delta2]

Because that's exactly the area where the magnetic field varies with time. Outside that area there is magnetic field (which is caused by the induced current on the 140 turn coil) but since the induced current is constant that magnetic field is constant too.

 

[ooohffff]

Because that's exactly the area where the magnetic field varies with time. Outside that area there is magnetic field (which is caused by the induced current on the 140 turn coil) but since the induced current is constant that magnetic field is constant too.

Ah, got it. Thanks!