Question

Two charged conducting spheres have radiir1 and r2 the ratio of their surface charge densities if their potentials are same is

Answer 1

V = K Q1 / R1 = K Q2 / R2

Q1 / Q2 = R2 / R1

If p is the surface density then p = Q / A = Q / (4 * pi * R^2)

p1 / p2 = (Q1 / R1^2) / (Q2 / R2^2) = (Q1 * R2^2) / (Q2 * R1^2)

p1 / p2 = (Q1 / Q2) * (R2 / R1)^2

Substituting for Q1 / Q2

p =  ( R2 / R1)  *   (R2 / R1)^2 = (R2 / R1)^3