Question

Two spherical conductors of radii 4m and 5 m are charged to the same potential . if

Answer 1

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A complete question is ------->Two spherical conductors of radii 4m and 5 m are charged to the same potential . if σ₁ and σ₂ are surface charge densities of spherical conductors then, find ratio of σ₁ to σ₂?

∵ both the spherical conductors charged to the same potential.
∴ potential of sphere₁ at surface = potential of sphere₂ at surface
⇒Kq₁/r₁ = Kq₂/r₂
⇒q₁/q₂ = r₁/r₂ ----(1)

Now, surface charge density of sphere₁ = q₁/4πr₁²
surface charge density of sphere₂ = q₂/4πr₂²

Now, σ₁/σ₂ = {q₁/4πr₁² }/{ q₂/4πr₂² } = (q₁/q₂)(r₂/r₁)² = (r₂/r₁) [from equation (1)

Now, put r₁ = 4cm and r₂ = 5cm
σ₁/σ₂ = (5/4) = 5/4

Answer 2

Potential of a spherical conductor is KQ/R, where K is a constant. For the potential of both the spheres to be equal, Q₁/R₁ = Q₂/R₂ ⇒ Q₁/Q₂ = R₁/R₂ = 4/5. If you wish to find out the ratio of surface charge densities, we can do that by dividing (Q₁/R₁²)÷(Q₂/R₂²) = (Q₁/Q₂)(R₂/R₁)² = 5/4.