Induced EMF: Solenoid in Square Loop

[triplebeem1]

Homework Statement

The solenoid has N turns of wire around a cylinder. The radius of the cylinder is "a" and length is "b." THe current of the solenoid varies as I(t)= I$$_{0}$$(1 - e^-$$\alpha$$t) . I$$_{0}$$ and $$\alpha$$ are positive constants. Around the solenoid is a square loop of wire with side length "c." The axis of the square loop is parallel to and coincides with the axis of the solenoid. What is the magnitude of the induced EMF in the square loop?

Homework Equations

$$\epsilon$$ = -N$$\frac{d\phi}{dt}$$

The Attempt at a Solution

$$\epsilon$$ = -N$$\frac{d\phi}{dt}$$

d$$\epsilon$$ = -N$$\frac{dBA}{dt}$$

$$\epsilon$$ = -NA$$\int$$dB

$$\epsilon$$ = (-NA)[($$\mu$$NI)/B]

 

[chaoseverlasting]

Thats not strictly correct. The magnetic field of the solenoid is not a constant which you can integrate as you did. You are given the constants a and b for a reason. You can find the magnetic field by using ampere's circuital law. That is what you must integrate.

 

[triplebeem1]

Would I need to use the B-field of the solenoid to find the electric flux and then finally the inductance? I think I'm having a hard time grasping the concept of the question. I'm assuming the solenoid and cylinder are the same. Is that what you assume as well?