Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): For a uniformly charged solid conducting sphere of radius R , the electric field at a distance r ( r > R ) from the center is given by VR r^2 , where V is the potential on the surface. Reason (R): The electric potential at a distance r > R from the center is given by V(r) = V ( R^2 r^2 ) , and the

Step-by-step solution

Assertion is true: The potential on the surface of the conducting sphere is V = 1 4 ₀ q R . The electric field outside the sphere at distance r > R is E = 1 4 ₀ q r^2 . Substituting q = 4 ₀ V R into the electric field expression gives E = V R r^2 . Reason is false: The electric potential outside the sphere at a distance r > R is V(r) = 1 4 ₀ q r . In terms of surface potential V , this is V(r) = V ( R r ) , not V ( R^2 r^2 ) . The electric field is indeed the negative gradient of the potential ( E = - dV dr ), but