Two metal spheres, one of radius R and the other of radius 2R, both have the same surface charge density σ. They are brought in contact and separated. What will be new surface charge densities on them?
Before contact, charges of each spheres, q1=σ4πR2;q2=σ4π(2R)2=4q1 When the two sphere are brought in contact, their charges are shared till their potentials become equal i.e., V1=V2 ∴4πε0Rq1′=4πε0(2R)q2′ ∴q2′=2q1′....(i) As there is no loss of charge in the process ∴q1′+q2′=q1+q2=q1+4q1=5q1=5(σ4πR2) or q1′+2q1′=5σ4πR2 (using (i)) q1′=35σ4πR2;q2′=2q1′=310(σ4πR2) σ1=4πR2q1′=35σ,σ2=4π(2R)2q2′=65σ
