SATHEE: electromagnetic-waves Question 20

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Question: Q. 11. A capacitor made of two parallel plates each of plate area $A$ and separation $d$ , is being charged by an external $a c$ source. Show that the displacement current inside the capacitor is the same as the current charging the capacitor.

U] [O.D. I, II, III 2013]

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Solution:

Ans.

$\begin{aligned} i_{d} & = \frac{d ϕ_{E}}{d t} & = ε_{0} \frac{d (E A)}{d t} \end{aligned}$

Electric field between the plates of a capacitor

$\begin{aligned} E & = \frac{σ}{ε_{0}} = \frac{q}{ε_{0} A} ∴ i_{d} & = \frac{ε_{0} A}{ε_{0} A} \frac{d q}{d t} i_{d} & = \frac{d q}{d t} = i \end{aligned}$

Where $i$ is the charging current. This proves that the displacement current inside the capacitor is the same as the current charging the capacitor.

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