A square conducting loop with sides of length L is rotation at a constant angular speed of, w (omega), in a uniform magnetic field of magnitude B. At time t=0, the loop is oriented so that the direction normal to the loop is aligned with the magnetic field. Find the expression for the potential difference induced in the loop as a function of time.
I think it's Vind= BL^2*w*sin(theta)
Is this right? If it's not, can someone please explain how it should be? Thanks.
To find the expression for the potential difference induced in the loop as a function of time, we can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced electromotive force (EMF) in a conducting loop is equal to the rate of change of magnetic flux through the loop.
The magnetic flux through the loop can be calculated by multiplying the magnetic field strength (B) by the area of the loop (A). In this case, since the loop is a square with sides of length L, the area can be given as A = L^2.
The direction normal to the loop is aligned with the magnetic field, so the magnetic flux is constant over time. Therefore, the rate of change of magnetic flux is zero, and there is no induced EMF.
As a result, the expression you provided (V_ind = BL^2w*sin(theta)) is not correct in this case. The potential difference induced in the loop is actually zero.
This is because the induced EMF depends on the rate of change of magnetic flux, and since the magnetic flux remains constant as the loop rotates in the uniform magnetic field, there is no change in the flux, and hence no induced EMF.
So, the correct expression for the potential difference induced in the loop as a function of time in this specific scenario is V_ind = 0.