Calculate the potential difference induced in the circuit as a function of time

[blueyellow]

Homework Statement

A square circuit with side L lies in the x-y plane, is centred on the origin and has sides parallel to the x and y axes. At time t=0 it starts turning about the x axis, in a region characterised by a uniform magnetic field B parallel to z, with uniform angular speed omega. By considering the angle between the surface normal and the field, calculate the potential difference (electromotive force) induced in the circuit as a function of time.

Homework Equations

phi(subscript B)=BA cos theta

potential difference=-d(phi (subscript b))/dt

The Attempt at a Solution

potential difference=-d(BA cos theta)/dt

this isn't leading anywhere. I don't know how to differentiate it with respect to t

 

[Pi-Bond]

You need to express the angle theta (angle between surface normal and field lines) in terms of time. (theta starts from 0 degrees)

 

[blueyellow]

thank you, Pi-bond

potential difference=-d(BA cos omega*t)/dt

=BA omega sin (omega*t)

correct?

 

[Pi-Bond]

Yes, that is correct.