State Gauss theorem in electrostatics. Prove that no electric field exists inside a hollow charged sphere.

Explanation

For Gauss theorem , refer under the heading " Chapter At A Glance " Consider a hollow charged conducting sphere of radius R and having charge Q .To find electric field at a point P inside the shell , consider a sphere through point P and having centre O, i.e. r= The electric flux through the Gaussian surface
` " " phi _in = oint oversetto E . hat n ds = E 4 pi r^(2) `
According to Gauss theorem, total electric flux should be
` " " phi _in =(1)/( in _0) ` (charged enclosed )= 0
[Since the Gaussian surface is not enclosing any charge]
Thus ` " " phi_in = E. 4 pi r^(2) =0 " " ...(ii) `
[Since the Gaussian surface is not enclosing any charge]
Thus ` phi _in =E. 4 pi r^(2) =0 `
`rArr " "E=0 `
Hence , no electric field exists inside a hollow charged sphere.