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  4. 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

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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 byPhysics Question Image

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Solution:

$I_{d}=\varepsilon_{0} A \frac{d E}{d t}=\varepsilon_{0}\left(\pi R^{2}\right) \frac{d E}{d t}=i$
$I_{d}'=\varepsilon_{0}\left(\pi R^{2}-\frac{\pi R^{2}}{4}\right) \frac{d E}{d t}$
$=\frac{3}{4} \varepsilon_{0} \pi R^{2} \frac{d E}{d t}$
$I_{d}'=\frac{3}{4} i$