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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