2. A square copper frame has sides of length b. A very long thin solenoid goes through the frame as shown. The solenoid has Ntums in a total length and radius a. Assume that > > 2a so the solenoid goes through the frame. The solenoid has an AC current given by I(t) = 1, sin(at) with cow counted as positive. The angular frequency w is constant. a. Write an expression for the magnetic flux through the square frame as a function of time. Hint: what is the magnetic field inside and outside a long solenoid? b. Determine the EMF induced in the frame as a function of time. Please use Faraday's Law with the minus sign. ONL 2a head on view b c. What is the amplitude of the induced EMF? The amplitude of a sinusoidal function is the maximum deviation of the function from the average value. Hint: what is the largest value that cosine or sine can have during a cyde? d. What is the induced EMF as a function of time if the square frame was small enough to fit entirely inside the solenoid (> <2a) as shown? You should be able to figure this out from without redoing all the work.

2. A square copper frame has sides of length b. A very long thin solenoid goes through the frame as shown. The solenoid has Ntums in a total length and radius a. Assume that > > 2a so the solenoid goes through the frame. The solenoid has an AC current given by I(t) = 1, sin(at) with cow counted as positive. The angular frequency w is constant. a. Write an expression for the magnetic flux through the square frame as a function of time. Hint: what is the magnetic field inside and outside a long solenoid? b. Determine the EMF induced in the frame as a function of time. Please use Faraday's Law with the minus sign. ONL 2a head on view b c. What is the amplitude of the induced EMF? The amplitude of a sinusoidal function is the maximum deviation of the function from the average value. Hint: what is the largest value that cosine or sine can have during a cyde? d. What is the induced EMF as a function of time if the square frame was small enough to fit entirely inside the solenoid (> <2a) as shown? You should be able to figure this out from without redoing all the work.