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.
Given-
Area of the plate= 100 cm2 = 0.01m
Separation between the plates = 0.500 cm = 5 × 10-3 m
Thickness of the metal, t = 4 × 10-3 m
We know capacitance is given by
Where
A= area of cross section
K = dielectric constant
d= separation between the slab and
∈0 = permittivity of free space = 8.85×10-12
t = Thickness of the metal
Since, it’s a metal, for metals k = infinite
Hence, capacitance is given by-
=
Here capacitance is a constant value, hence the capacitance
is independent of the position of the metal.
At any position, the net separation is d − t).