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) = a - bt, where a = 18 V/m and b = 9 V/(m s) and is confined to a circular area with a radius R = 4 meters. What is the magnitude and direction of the magnetic field (in picoTesla) at a point P on the circumference of the circle at the time t = 2 seconds? 

Answer 1

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

If I choose my orientation to by counter-clockwise then ΦE = Eπr² and

and solving for B gives 

Since B is negative it points opposite the direction of my orientation (clockwise).