State Gauss's theorem. Obtain an expression for elactric field at any point outside a charged spherical hollow conductor (shell).

Explanation

Gauss's theorem: The total outward electric flux passing through a closed surface in air is `(1/(epsilon_(0)))` times the total charge enclosed by it.
Let +Q be the charge enclosed by a hollow conductor of radius R.

Let p be a point at a distance r from the centre of the conductor Let ds a small element of area surrounding the point. A normal drawn from the point coincides with the direction of `vecE`. Hence `cos 0^(@)=1`.
From Gauss's theorem,
TOFF `=phi=(1/(epsilon_(0)))Q`.........1
By definition `phi=E cos theta Sigma ds`.
where `sumds=4 pi r^(2), cos theta=cos 0^(@)=1`
Hence `phi=E.4pir^(2)`..........2
comparing 1 and 2
we write `E=(1/(4 pi epsilon_(0)))Q/(r^(2))`
For point on the surface `r=R`
`E=(1/( 4 pi epsilon_(0)))(Q/(R^(2)))`
This electric field intensity is maximum. Since electric flux depends on the charge enclosed and electric field intensity depends on the electric flux, electric field remains zero at all points inside the sphereical hollow conductor.