Question

The separation between the plates of a parallel-plate capacitor is 0⋅500 cm and its plate area is 100 cm2. 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.

Answer 1

Explanation:

To Show: The capacitance of the assembly is independent of the position of the metal plate within the gap and find its value.

Given

Area of the plates = 100 $cm^2$

Separation between plates = 0.500 cm = 5 X $10^{-3}$

Thickness of the metal (t) = 4 X $10^{-3}$ m

Capacitance (C) = $C=\frac{\epsilon_{0} A}{d-t+\frac{t}{k}}$

where,

K= Dielectric constant of the metal

d = separation of the plates

t  = thickness of the plates

For metal, K = infinity

After substituting the values, C= 88 pF

Hence, we can say that, here the capacitance is always independent of the position of the metal.

At any position in the circuit, the net separation = (Distance d – time t).