A parallel plate capacitor with circular plates of radius R is being charged as shown in the figure. Let B(r) be the induced magnetic field at a distance r from the central axis between the plates. Assuming d R , the ratio B(2d) B(d) , while charging, is

Step-by-step solution

Inside the parallel plate capacitor, the electric field E is uniform and changes with time as the capacitor charges. According to the Ampere-Maxwell law, the induced magnetic field B along a circular loop of radius r (where r B d l = ₀ ₀ d _E dt B(r) 2 r = ₀ ₀ d dt (E r^2) B(r) 2 r = ₀ ₀ r^2 dE dt B(r) = ₀ ₀ r 2 dE dt Since dE dt is constant across the cross-section, the induced magnetic field B(r) is directly proportional to the distance r from the central axis, i.e., B(r) r . Given d R , both points at distances