When a charge Q is given to an isolated metal plate X of surface area A, its surface charge density becomes sigma . When an earthed parallel metal plate is brought close to the X . Find the magnitude of surface charge density on inner side of X.

Asked by vinitapahel123 | 1st Jul, 2015, 06:43: PM

Expert Answer:

Consider an isolated metal plate X of surface area A. We know that in isolated plate, uniform distribution of charge takes place on the 2 surfaces by Q/2, Q/2
Hence, the surface charge density becomes, σ = Q/2A
Now, when another earthed parallel metal plate is brough close to the X, outer surface charge of other plate will become zero.
Hence, outer surface of plate X and inner surface of other plate will become +Q and - Q respectively as shown in figure.
So the final surface charge density becomes,
begin mathsize 12px style straight sigma subscript straight f equals straight Q over straight A since. space straight sigma equals fraction numerator straight Q over denominator 2 straight A end fraction rightwards double arrow straight sigma subscript straight f equals straight Q over straight A equals 2 straight sigma end style

Answered by Priyanka Kumbhar | 2nd Jul, 2015, 09:23: AM