Magnetic field between circular capacitor plates (${\tilde{B}}_{\varphi }(s)=-i\omega {\mu }_0{ϵ}_0{V}_{0}s/(2d)$)

For a circular air-filled parallel-plate capacitor with voltage phasor $V_0{e}^{-i\omega t}$, uniform gap $d$ and radius $a$, the Ampère-Maxwell equation on a circular loop of radius $s<a$ gives the displayed magnetic field. The enclosed displacement current is proportional to $s^2$, whereas the circulation is $2\pi s{B}_{\varphi }$. Consequently its amplitude grows linearly from zero on the axis. This assumes negligible fringing fields and a quasistatic approximation $\omega a/c\ll 1$.