The magnetic field inside a circular parallel plate capacitor of radius R is observed to be directly proportional to the radial distance r from the central axis. If the magnitude of this magnetic field at any fixed point inside the capacitor is constant in time, what is the time dependence of the electric field E between the plates?

Step-by-step solution

According to the Ampere-Maxwell law, the magnetic field B inside the capacitor at a radial distance r is given by B d l = ₀ I_ d, enclosed . Since the enclosed displacement current I_ d, enclosed = J_d ( r^2) , we have B(2 r) = ₀ J_d r^2 B = ₀ J_d r 2 . We are given that B is constant in time at any fixed point r . This implies that the displacement current density J_d must be constant in time. The displacement current density is related to the electric field by J_d = ₀ dE dt . For J_d to be a non-zero constant, th