Ask a Teacher

Search



Q4.Using Gauss theorem,show mathematically that,for any point outside the shell,the electric field due to an uniformly charged thin spherical shell is the same as if the entire charge of the shell is concentrated at its center.Why do you expect the electric field inside the shell to be zero according to this theorem??
Consider a thin spherical shell of radius R and centre O. Let +q be the inform charge on the surface of the sphere. 
We are to find the electric field intensity at any point poolside the shell where OP = r. With O as centre, draw a sphere of radius r through point P as shown in the figure. Then this sphere is the Gaussian surface. The electric flex passing through the spherical shell will be the same as that of through the Gaussian surface. The magnitude of electric field(E) is same at all points on the Gaussian surface. Further, at every point on the Gaussian surface, angle between   and area element rector   is zero. Therefore, electric flex passing through the Gaussian surface is
This is the same field intensity which a point charge +q placed at 0 would set up at a point P. 
Thus, electric field intensity at any point outside a uniformly charged spherical shell is the same as if all the charge were concentrated as a point charge at the centre of the shell. 


comments powered by Disqus