We know from Ampere'* 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.