Using Gauss's theorem show mathematically that for any point outside the shell , the field due to a uniformaly charged thin spherical shell is the same as if the entire charge of the shell is concentrated at the centre? Why do you expect the electric field inside the shell to be zero according to this theorem?

Explanation

To show that at any point outside the spherical shell electric field is same as if whole charge of shell is concentreated at the centre , see Short Answer Question number 40. At the point inside the shell , according to Gauss theorem, we expect the electric field to be zero because there is no charge present inside. Hence electric flux and consequently electric field at that point will be zero.