A parallel plate capacitor with circular plates of radius R is being charged as shown. At the instant shown, the displacement current in the region between the plates enclosed between (R/2) and R is given by

Question

A parallel plate capacitor with circular plates of radius R is being charged as shown. At the instant shown, the displacement current in the region between the plates enclosed between (R/2) and R is given by (A) (3/4) i (B) (1/4) i (C) 3 i (D) (4/3) i

Tardigrade Admin · Accepted Answer

Id=ε0 A (d E/d t)=ε0(π R2) (d E/d t)=i Id'=ε0(π R2-(π R2/4)) (d E/d t) =(3/4) ε0 π R2 (d E/d t) Id'=(3/4) i

Q. A parallel plate capacitor with circular plates of radius $R$ is being charged as shown. At the instant shown, the displacement current in the region between the plates enclosed between $\frac{R}{2}$ and $R$ is given by

$\frac{3}{4} i$

$\frac{1}{4} i$

$3 i$

$\frac{4}{3} i$

$I_{d} = ε_{0} A \frac{d E}{d t} = ε_{0} (π R^{2}) \frac{d E}{d t} = i$
$I_{d}^{'} = ε_{0} (π R^{2} - \frac{π R ^{2}}{4}) \frac{d E}{d t}$
$= \frac{3}{4} ε_{0} π R^{2} \frac{d E}{d t}$
$I_{d}^{'} = \frac{3}{4} i$

Q. A parallel plate capacitor with circular plates of radius R is being charged as shown. At the instant shown, the displacement current in the region between the plates enclosed between 2R​ and R is given by

43​i

41​i

3i

34​i