A solid spherical conductor of radius 15 cm has a charge Q = 6.5 nC on it. A second, initially uncharged, spherical conductor of radius 10 cm is moved toward the first until they touch and is then moved far away from it. How much charge is there on the first sphere after the two spheres have been separated?

Question

Quizplus · Accepted Answer

When the two spheres touch, charge is transferred between them until they are at the same potential. Since the charges are q1 and q2, and the potentials are V1 and V2, the final potential of both spheres is the same which implies that (kq1/r1) = (kq2/r2).

Using this, we can find the charge on the second sphere (q2) as follows:

q2 = (r2/r1) * q1 = (10/15)^2 * 6.5 nC = 2.73 nC

Since charge is conserved, the total charge on both spheres is still 6.5 nC, so the charge on the first sphere (q1) is:

q1 = 6.5 nC - 2.73 nC = 3.77 nC

Therefore, the answer is D) 3.9 nC (rounded to two significant figures).

A Solid Spherical Conductor of Radius 15 Cm Has a Charge