# Induced EMF: Solenoid in Square Loop

## 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]