Question 682: Electrostatics & Capacitance

Question

A parallel plate capacitor with plate area $A$ and separation 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 simultaneously between the plates. The displacement current through this area is

Accepted Answer

Charge on capacitor plates at time $t$ is given as, $q=it$.
Electric field between the plates at this instant.
$E=\frac{q}{A \varepsilon_0}=\frac{i t}{A \varepsilon_0}$
Electric flux through the given area
$\phi_E=\left(\frac{A}{2}\right) E=\frac{i t}{2 \varepsilon_0}$
Thereiore, displacement current,
$i_d=\varepsilon_0 \frac{d \phi_E}{d t}=\varepsilon_0 \frac{d}{d t}\left(\frac{i t}{2 \varepsilon_0}\right)=\frac{i}{2}$

Answer

$i$

Answer

$i/2$

Answer

$i/4$

Answer

$i/8$

Electrostatics & Capacitance

A parallel plate capacitor with plate area A and separation 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 simultaneously between the plates. The displacement current through this area is

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