Question

Sphere 1 with radius R1 has positive charge q. Sphere 2 with radius 7.0R1 is far from sphere 1 and initially uncharged. After the separated spheres are connected witha wire thin enough to retain only negligible charge, what fraction of q ends up on (a) sphere 1 and (b) sphere 2? (c) What is the ratio of the final surface chargedensity of sphere 1 to that of sphere 2? (Answer with 2 significant figures.)

Answer 1

The spheres connected with a same wire. So, potential is same for both spheres. The total charge of the system of two spheres equal to sum of individual charges on two spheres because the spheres are connected with a wire. The potential of first sphere is, The potential of second sphere is, Equate and V 91 The radius of second sphere is 6/R 6R Substitute q in equationq qh+g Substitute g in g.

The surface charge density of the first sphere is, g1 A4 4T The surface charge density of the second sphere is, 92 g2 Ax The ratio of the surface charge density of two sphere is, 92 4x R,2 91 41 -6.0