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A conducting sphere of radius $r$ has a charge. Then
The charge is uniformly distributed over its surface, if there is an external electric field.
Distribution of charge over its surface will be non uniform if no external electric field exist in space.
Electric field strength inside the sphere will be equal to zero only when no external electric field exists
Potential at every point of the sphere must be same
Solution
From the basic properties of conductors we can say that any charge is always uniformly distributed over the surface of the conductor without any external field. The electric field inside the spherical conductor is always zero and the surface of the conductor is an equipotential surface. So the potential at every point of the sphere is same.
