Two metal sphere of radius R and 3R have same surface charge density . If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes ₁ and ₂ , respectively. The ratio ₁ ₂ is.

Step-by-step solution

When the two metal spheres are brought in contact and separated, they acquire the same electric potential. Let the final surface charge densities be ₁ and ₂ . The potential of a conducting sphere of radius r and surface charge density ' is given by V = 1 4 ₀ q r = 1 4 ₀ ' (4 r^2) r = ' r ₀ Equating the final potentials of the two spheres: V₁ = V₂ ₁ R ₀ = ₂ (3R) ₀ ₁ R = 3 ₂ R ₁ ₂ = 3 Answer: 3