A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its plates is increasing at a constant rate with time. The magnetic field arising due to displacement current is :
Answer: (C) non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates
The displacement current $I_d = \epsilon_0\dfrac{d\phi_E}{dt}$ is constant and spread uniformly over the plate area (radius $R$).
Ampère–Maxwell law at distance $r$ from the axis:
Inside ($r < R$): $B \cdot 2\pi r = \mu_0 I_d\dfrac{r^2}{R^2}$, so $B = \dfrac{\mu_0 I_d r}{2\pi R^2}$, which increases with $r$.
Outside ($r > R$): $B = \dfrac{\mu_0 I_d}{2\pi r}$, which decreases with $r$.
So $B$ is non-zero everywhere (except on the axis) and is maximum at $r = R$, the cylindrical surface joining the edges of the plates.
Solution by Sreeraj P, M.Sc Physics