Question

A parallel plate capacitor consists of circular plates with radius $$10 cm$$ , separated by a distance of $$0.5mm$$. The capacitor is charged by an external source such that the electric field between the plates changes at a rate $$5 \times 10^{13} Vm{-1}s{-1}$$. The displacement current through the capacitor is

A
1.4mA
B
14mA
C
14A
D
1.4A

Solution

The correct option is B $$14 A$$Displacement current $$=\dfrac{dQ}{dt}=\dfrac{d(CV)}{dt}$$$$=C\dfrac{dV}{dt}\\ =C(d.\dfrac{dE}{dt})$$$$=\dfrac{A\epsilon_0}{d}.d\dfrac{dE}{dt}$$$$=A\epsilon_0\dfrac{dE}{dt}$$$$=\pi r^2 \epsilon_0\dfrac{dE}{dt}$$$$=14A$$Physics

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