Two isolated conducting spheres of radii R and 3R initially have the same surface charge density σ. They are brought into contact and then separated. If the final surface charge densities on the smaller and larger spheres are σ₁ and σ₂ respectively, the ratio σ₁/σ₂ is:
Options

Question

Two isolated conducting spheres of radii R and 3R initially have the same surface charge density σ. They are brought into contact and then separated. If the final surface charge densities on the smaller and larger spheres are σ₁ and σ₂ respectively, the ratio σ₁/σ₂ is:

Options

G1 Physics · Accepted Answer

After contact, the two conducting spheres come to the same potential. For a conducting sphere, V = kQ/r. Since Q = 4πr²σ, V = 4πk rσ. Thus equal potentials imply σ₁r₁ = σ₂r₂. Here, r₁ = R, r₂ = 3R. Therefore, σ₁R = σ₂(3R) ⇒ σ₁/σ₂ = 3. Correct option: D.