Question

Consider the situation illustrated in the Figure. A uniform electric field points in the z-direction (out of the paper) with a value given by E_z(t) = at, and a uniform magnetic field points in the z-direction with a value given by B_z(t) = bt. Both fields are confined to a circular region with a radius R. If a = 1 V/(m s) and b = 1 T/s and if the magnitude of the induced electric field at the point P on the circumference of the circle at the time t = 2 seconds is 9,000 V/m, what is the magnitude induced magnetic field (in picoTesla) at the point P at the time t = 2 seconds?

Answer 1

We know from Ampere's Law (with I_enclosed = 0) that

choose my orientation to by counter-clockwise then Φ_E = EπR² and 

and solving for the induced magnetic field B gives

Now from Faraday's Law we know that

If I choose my orientation to by counter-clockwise then Φ_B = BπR² and

and solving for the magnitude of the induced electric field E gives