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:

1. Displacement Current ($I_d$):
Charging the capacitor changes the electric field $E$ between the plates. $E=\frac{\sigma }{{ϵ}_0}$. Since $\frac{d\sigma }{dt}$ is constant, $\frac{dE}{dt}$ is constant.
Displacement current density $J_d={ϵ}_0\frac{\partial E}{\partial t}$.2. Magnetic Field ($B$):
According to Ampere-Maxwell law, $\oint \vec{B}\cdot d\vec{l}={\mu }_0{I}_d$.
For a circular path of radius $r$ inside the plates ($r\le R$, where $R$ is plate radius):$B(2\pi r)={\mu }_0(J_d\cdot \pi r^2)⟹B\propto r$.
For $r>R$ (outside):$B(2\pi r)={\mu }_0(J_d\cdot \pi R^2)⟹B\propto \frac{1}{r}$.3. Observation:
The field $B$ increases linearly from zero at the center ($r=0$) to a maximum at the edge ($r=R$), and then decreases outside. Thus, the field is non-zero everywhere (except at the exact axis) and peaks at the periphery.