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# A parallel plate capacitor with plate area $A$ and separation $d$ between the plates is charged by a constant current $i$. Consider a plane surface of area $\large\frac{A}{2}$ parallel to the plates and drawn symmetrically between the plates. Find the displacement current through this area.

$\begin {array} {1 1} (a)\;i & \quad (b)\;\large\frac{i}{4} \\ (c)\;\large\frac{i}{3} & \quad (d)\;\large\frac{i}{2} \end {array}$

$\phi_E = \large\frac{EA}{2}$$= \large\frac{Q}{(\in_o A)}$$ \times \large\frac{A}{2}$
$= \large\frac{Q}{2\in_o}$
$I_D = \in_0\: \large\frac{d(\phi E)}{dt}$$= \large\frac{\in_oi}{2\in_o}$$ = \large\frac{i}{2}$
Ans : (d)