Two solid spherical conductors, A and B, have radii R and 2R respectively. Both spheres have the same uniform surface charge density . Let E_A be the magnitude of the electric field at a distance of 3R from the centre of sphere A, and E_B be the magnitude of the electric field at a distance of 4R from the centre of sphere B. The ratio E_A : E_B is:

Step-by-step solution

For a spherical conductor of radius r₀ and surface charge density , the total charge is Q = (4 r₀^2) . The electric field at a distance r ( r r₀ ) from the centre is given by: E = 1 4 ₀ Q r^2 = 1 4 ₀ (4 r₀^2) r^2 = r₀^2 ₀ r^2 For sphere A, radius r₀ = R and distance r = 3R : E_A = R^2 ₀ (3R)^2 = 9 ₀ For sphere B, radius r₀ = 2R and distance r = 4R : E_B = (2R)^2 ₀ (4R)^2 = (4R^2) ₀ (16R^2) = 4 ₀ Taking the ratio: E_A E_B = / 9 ₀ / 4 ₀ = 4 9 Answer: 4 : 9