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Q.

A dielectric slab of length l, width b, thickness d and dielectric constant K fills the space inside a parallel plate capacitor. At t = 0, the slab begins to be pulled out slowly with speed v. At time t, the capacity of the capacitor is

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a

$\frac{ε_{0} b}{d} [Kl - (K - 1) vt]$

b

$\frac{ε_{0} b}{b} [Kl + K + vt]$

c

$\frac{ε_{0} b}{b} [(Kl + 1) vt]$

d

$\frac{ε_{0} b}{d} [l + (K - 1) vt]$

answer is A.

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Detailed Solution

Question Image

$x = vt$

$C = \frac{ε_{0} bx}{d} + \frac{{Kε}_{0} b (l - x)}{d}$

$C = \frac{ε_{0} b}{d} (x + K (l - x))$

$= \frac{ε_{0} b}{d} [Kl - (K - 1) vt]$

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