The voltage across a parallel$-$plate capacitor with area A and separation $d$ varies with time as $V(t)=V_{0}sint.$

a$.$ Find the displacement current between the plates. $(4)$

b$.$ Show that this is equal to the current in the circuit which is equal to the time derivative of the charge on the capacitor. $(3)$

c$.$ If the direction of the current at some time $t$ is $-$hat$(),$ what is the magnetic field $($magnitude and direction$)$ at a distance $r$ from the wire? $(3)$

d$.$ What is the magnitude of the induced electric field at this same point?