Find out the maximum charge on an unearthed hollow metal sphere of radius 3.0m for which it would not discharge into air. What would be the potential of the sphere in that condition? Assume that, electric discharge into air initiates at a field intensity of `3xx10^(6)V cdot m^(-1)`.

Explanation

The electric field on the surface of a metal sphere of radius r having a charge q,
`E = 1/(4 pi epsilon_(0)) q/(r^2)`
The maximum charge `q_(m)` on the sphere, without any discharge into air, corresponds to `E = 3 xx 10^(6) V cdot m^(-1)`.
`:. 1/(4 pi epsilon_(0)) (q_m)/(r^3) = 3 xx 10^(6)`
or `q_(m) = (3xx10^(6)r^(2))/(1//(4pi epsilon_(0))) = (3 xx 10^(6)xx(3.0)^(2))/(9xx10^(9)) = 3 xx 10^(6)V`.