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.

NCERT Class XII
Physics - Exemplar Problems

Chapter 2. Potential and Capacitance

Answer 1

Potential of conducting spheres on the surface can be:
                V = 1/(4πε) * Q / R

So if the two spheres are at the same potential, then the charge on the larger sphere is more than that on the smaller sphere.
               V1 = V2  =>  Q1 / R1  = Q2/ R2
   =>  ρ1 * 4 π R1³ / (3 R1)   = ρ2 * 4 π R2³ / (3 R2)
   =>    ρ1 / ρ2  =  R2² / R1²

     If R1 > R2,  then    ρ1  < ρ2