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.

Question

Philoid · Accepted Answer

Lets consider the sphere of radius R₁ and charge Q₁ on it and the sphere of radius R₂ and charge Q₂ on it.

potential of conducting sphere on the surface can be written as

so if two sphere are at same potential, then the charge on the large sphere is more than that on the smaller sphere

therefore, ⇒ = =

W.K.T charge density

Therefore charge

⇒

As ⇒

Therefore, the charge density of the smaller sphere is more than that of the larger one

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.