Two solid conducting spheres of radii R and 2R are given charges such that their surface charge densities are equal. The ratio of their electric potentials, V₁ : V₂ , will be:

Step-by-step solution

The electric potential at the surface of a conducting sphere is V = 1 4 ₀ Q r . The charge Q on a sphere can be expressed in terms of its surface charge density as Q = 4 r^2 . Substituting this into the potential formula gives: V = 1 4 ₀ 4 r^2 r = r ₀ Since the surface charge density is the same for both spheres, the electric potential is directly proportional to the radius ( V r ). Therefore, the ratio of their potentials is: V₁ V₂ = R 2R = 1 2 The ratio is 1 : 2 . Answer: 1 : 2