Question

The potential difference, V_C, across a 3 Farad parallel-plate capacitor whose plates have radius R = 2 cm varies with time and is given by V_C(t) = at, with a = 10 V/s. What is the magnitude of the magnetic field (in microT) between the plates of the capacitor a distance R from the center? 

Answer 1

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

 

If I choose a loop of radius R within the capacitor then ΦE = EπR² and

where I have used E = Q/(ε0A), A = πR², and I = dQ/dt. Solving for B gives

where I used Q = CV which implies that dQ/dt = C dV/dt with dV/dt = a.