A hollow metal sphere of radius R is uniformly charged. What is the ratio of the electric potential at a distance of R 2 from the centre to the electric potential at a distance of 2R from the centre?

Step-by-step solution

For a uniformly charged hollow metal sphere of radius R and charge Q : The electric potential at any point inside the sphere ( r V_ inside = 1 4 ₀ Q R The electric potential at a point outside the sphere ( r > R ) is inversely proportional to the distance from the centre. At a distance r = 2R , the potential is: V_ outside = 1 4 ₀ Q 2R Taking the ratio of the two potentials: V_ inside V_ outside = 1 4 ₀ Q R 1 4 ₀ Q 2R = 1 1 2 = 2 Thus, the ratio is 2 : 1 . Answer: 2 : 1