A parallel-plate capacitor is formed by two plates, each of area 100 cm2  separated by a distance of 1 mm. A dielectric of dielectric constant 5.0 and dielectric strength 1.9×107Vm−1 is filled between the plates. Find the maximum charge that can be stored on the capacitor without causing any dielectric breakdown.

# A parallel-plate capacitor is formed by two plates, each of area   separated by a distance of 1 mm. A dielectric of dielectric constant 5.0 and dielectric strength $1.9×{10}^{7}{\mathrm{Vm}}^{-1}$ is filled between the plates. Find the maximum charge that can be stored on the capacitor without causing any dielectric breakdown.

1. A

$8.4×{10}^{-6}\mathrm{C}$

2. B

$9×{10}^{-6}\mathrm{C}$

3. C

$11×{10}^{-6}C$

4. D

10 C

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### Solution:

If Q be the charge on the capacitor, the surface charge density is $\mathrm{\sigma }=\mathrm{Q}/\mathrm{A}$

and the electric field is $\frac{\mathrm{Q}}{{\mathrm{KA\epsilon }}_{0}}$ .

This should not exceed the dielectric strength $1.9×{10}^{7}{\mathrm{Vm}}^{-1}$

Thus, the maximum charge is given by  $\frac{\mathrm{Q}}{{\mathrm{KA\epsilon }}_{0}}=1.9×{10}^{7}{\mathrm{Vm}}^{-1}$
Or, $\mathrm{Q}={\mathrm{KA\epsilon }}_{0}×1.9×{10}^{-7}{\mathrm{Vm}}^{-1}$
$=\left(5.0\right)\left({10}^{-2}{\mathrm{m}}^{2}\right)\left(8.85×{10}^{-12}{\mathrm{Fm}}^{-1}\right)×\left(1.9×{10}^{7}{\mathrm{Vm}}^{-1}\right)=8.4×{10}^{-6}\mathrm{C}$
.

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