a simple but important problem(charge density)[level1]

Physics

Two isolated metallic solid spheres of radii R and 2R are charged such that both of these have same charge density . The spheres are located far away from each other, and connected by a thin conducting wire. Find the new charge density on the bigger sphere. Solution: For sphere of radius R q1 = x 4R2 For sphere of radius 2R q2 = x 16 R2 When the two spheres are connected then the potential on the two spheres will be same. There will be a rearrangement of charge for this to happen. Let q'1 and q'2 be the new charges on the two spheres. Since the total charge remains the same q'1 + q'2 = q1 + q2 = x 20 R2 Also Since V1 = V2 ............(i) ............(ii) Substituting the value of q1' from (ii) in (i) + q'2 = x 20 R2 x 20 R2 New charge density on bigger sphere =