Question

Consider two conducting spheres of radii R₁ and R₂ with R₁ > R₂. If the two are at the same potential, the larger sphere has more charge than the smaller sphere. State whether the charge density of the smaller sphere is more or less than that of the larger one.

Answer 1

Since two spheres are at the same potential, therefore V₁ = V₂

⇒ Larger sphere has more charge

Now, 

Since R₁ > R₂, therefore σ₂ > σ₁.

Charge density of smaller sphere is more than that of larger one.