A parallel plate capacitor with plate are A and seperation betwee…

MCQ

A parallel plate capacitor with plate are $A$ and seperation between the plates $d$, is charged by a constant current $i$, consider a plane surface of area $A/2$ parallel to the plates and drawn symmetrically between the plates, the displacement current through this area, will be.

A
$i$
✓
$\frac{i}{2}$
C
$\frac{i}{4}$
D
None of these

✓

Answer

Correct option: B.

$\frac{i}{2}$

b
(b) Suppose the charge on the capacitor at time $t$ is $Q$, the electric field between the plates of the capacitor is $E = \frac{Q}{{{\varepsilon _0}A}}.$ The flux through the area considered is ${\phi _E} = \frac{Q}{{{\varepsilon _0}A}}.\frac{A}{2} = \frac{Q}{{2{\varepsilon _0}}}$
$\therefore$ The displacement current
${i_d} = {\varepsilon _0}\frac{{d{\phi _E}}}{{dt}} = {\varepsilon _0}\left( {\frac{1}{{2{\varepsilon _0}}}} \right)\frac{{dQ}}{{dt}} = \frac{i}{2}.$

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