In case of field outside a uniformly charged sphere, the charge can be assumed to be concentrated at the centre at the sphere . How can you prove it.

Explanation

Let a sphere of radius r is changed uniformly with charge q. A point P is taken outside the sphere at a distance `x(x gt r)` from the centre of the sphere.

To evaluate the electric field intensity at point P, let us imagine a spherical Gaussian surface concentric to the original conducting sphere.
If E be the intensity of electric field at a point on the spherical Gaussian surface of radius x, then,
total electric flux `=E*4pi x^(2)`
According to the Gauss' theorem (in SI)
total electric flux `=(q)/(in_(0))`
`therefore E* 4pi x^(2)=(q)/(in_(0)) or, E=(1)/(4pi in_(0))*(q)/(x^(2))`
again, if a charge q is imagined at the centre of sphere of radius x, then from Coulomb's law (in SI)
`E=(1)/(4pi in_(0))*(q)/(x^(2))` ltbtgt Therefor, in case of electric field outside a uniformly charged sphere, the charge can be assumed to be concentrated at the centre of the sphere.