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.
Correct option is B) Here, V1=V2or4πε0R1q1=4πε0R2q2 ∴q2q1=R2R1...(i) Given R1>R2 ∴q1>q2 ∴ Larger sphere has more charge than the smaller sphere. Now charge densities σ1=4πR12q1;σ2=4πR22q2 ∴σ1σ2=q1q2R22R22orσ1σ2=R1R2R22R12=R2R1 (using (i)) As R1>R2, therefore σ2>σ2 Charge density of smaller sphere is more than the charge density of larger sphere
