A parallel plate capacitor having square plate of area a and separation between plates d is completely filled with a dielectric of dielectric constant k. Capacitor is connected with a battery of potential difference V. Now dielectric is pulled with constant speed u. Find the initial value of current.

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$\frac{V \sqrt{a} {uε}_{0}}{d} [k - 1]$

$\frac{V \sqrt{a} {uε}_{0}}{2 d} [k - 1]$

$\frac{2V \sqrt{a} {uε}_{0}}{d} [k - 1]$

Zero

answer is B.

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Detailed Solution

$C = \frac{k \sqrt{a} (\sqrt{a} - x) ε_{0}}{d} + \frac{\sqrt{a} {xε}_{0}}{d}$
$Q = CV = \frac{V \sqrt{a} ε_{0}}{d} [k (\sqrt{a} - x) + x]$
$I = |\frac{dQ}{dt}| = V |\frac{dC}{dt}| = |\frac{V \sqrt{a} ε_{0}}{d} [- k + 1] \frac{dx}{dt}|$
$I = \frac{V \sqrt{a} {uε}_{0}}{d} [k - 1]$ (constant)
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