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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 $$\dfrac{A}{2}$$ parallel to the plate and down symmetrically between the plates. Find the displacement current through this area. 


A
id=i8
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B
id=i2
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C
id=i3
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D
id=i4
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Solution

The correct option is B $$i_d= \dfrac{i}{2}$$
Displacement current $$=\dfrac{dQ}{dt}=\dfrac{d(CV)}{dt}$$
$$=C\dfrac{dV}{dt}=C(d.\dfrac{dE}{dt})$$
$$=\dfrac{A\epsilon_0}{d}.d\dfrac{dE}{dt}$$
$$=A\epsilon_0\dfrac{dE}{dt}\propto A$$
Hence, current halves when area of plates halves.

Physics

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