The separation between the plates of a parallel-plate capacitor is 0.500 cm and its plate area is $100 c m^{2} .$ A 0.400 cm thick metal plate is inserted into the gap with its faces parallel to the plates. Show that the capacitance of the assembly is independent of the position of the metal plate within the gap and find its value.

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Solution

Plate area = $100 c m^{2}$

$= 100 \times 10^{- 4} m^{2}$

$= 10^{- 2} m^{2}$

Separation d = 5 mm

$= 5 \times 10^{- 3} m,$

Thickness of metal,

$t = 4 c m = 4 \times 10^{- 2} m$

So, $C = \frac{\in_{0} K A}{d}$

Here, K = deelectric of a metal

$t = \frac{t}{k} = 0$

Here, the capacitance is independent of the position of metal. At any position the net separation is d - t, where d is the separation and t is thickness.

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