Concentric metallic hollow spheres of radii R and 4R hold charges Q 1 and Q 2 respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V R - V ( 4 R ) is:

Step-by-step solution

As given the surface charge density for both the spheres is same, hence           σ 1 = σ 2 ∴ Q 1 A 1 = Q 2 A 2 ⇒ Q 1 4 π R 2 = Q 2 4 π 4 R 2 ∴ Q 2 = 16 Q 1 From above diagram, the electric potential for both the spheres is V Inner = KQ 1 R + KQ 2 4 R = K R Q 1 + 16 Q 1 4 = 5 KQ 1 R . In the same way for outer sphere, V Outer = KQ 1 4 R + KQ 2 4 R = K 4 R 16 Q 1 + Q 1 = 17 KQ 1 4 R . Now the potential difference is, ∆ V = V inner - V outer = 5 KQ