Obtain the expression of electric field by thir spherical shell with uniform charge distribution at a point outside it.

Explanation

Let `sigma` be the uniform surface charge density of thin spherical shell of radius R.

Consider a point P outside the shell with radius vector `vecr`.
To calculate `vecE` at P, we take the Gaussian surface to be a sphere of radius t and with centre 0 passing through P.
The electric field at each point of the Gaussian surface has the same magnitude E and is along the radius vector at each point.
Thus, `vecE` and `DeltavecS` at every point are parallel and the flux through each element is `EDeltaS`.
Summing over all `DeltaS` the flux through the Gaussian surface is `E xx 4pir^(2)`.
The charge enclosed is `sigma xx 4piR^(2)`
By Gauss.s law, `E xx 4pir^(2) = sigma/epsilon_(0).4piR^(2)`
`therefore E = (sigmaR^(2))/(epsilon_(0)r^(2)) =q/(4piepsilon_(0)r^(2)) =(kq)/r^(2)`
`therefore vecE = (sigmaR^(2))/(4pi epsilon_(0)r^(2))hatr = (kq)/r^(2).hatr`