In Frame 1, two identical conducting spheres, A and B, carry equal amounts of excess charge that have the same sign. The spheres are separated by a distance d; and sphere A exerts an electrostatic force on sphere B that has a magnitude F. A third sphere, C, which is handled only by an insulating rod, is introduced in Frame 2. Sphere C is identical to A and B except that it is initially uncharged. Sphere C is touched first to sphere A, in Frame 2, and then to sphere B, in Frame 3, and is finally removed in Frame 4. Determine the magnitude of the electrostatic force that sphere A exerts on sphere B in Frame 4.

Question

In Frame 1, two identical conducting spheres, A and B, carry equal amounts of excess charge that have the same sign. The spheres are separated by a distance d; and sphere A exerts an electrostatic force on sphere B that has a magnitude F. A third sphere, C, which is handled only by an insulating rod, is introduced in Frame 2. Sphere C is identical to A and B except that it is initially uncharged. Sphere C is touched first to sphere A, in Frame 2, and then to sphere B, in Frame 3, and is finally removed in Frame 4.  Determine the magnitude of the electrostatic force that sphere A exerts on sphere B in Frame 4.

Quizplus · Accepted Answer

When sphere C is touched to sphere A, the excess charge on A is shared by C and the magnitude of the electrostatic force that A exerts on B decreases by a factor of 2 (since the charge on A is reduced by half).

When sphere C is then touched to sphere B, the excess charge on B is shared by C and A, so the net charge on sphere A increases while the net charge on sphere B decreases. The magnitude of the electrostatic force that A exerts on B is proportional to the product of their charges (Q_AQ_B/d^2), so the force decreases by a factor of (Q_A-deltaQ)(Q_B+deltaQ)/Q_AQ_B = (Q_A^2 - deltaQ^2)/(Q_AQ_B + deltaQ*Q_A).

Since deltaQ = Q_A/2, this expression becomes (3/4)Q_A^2/(Q_AQ_B + (3/8)Q_A^2) = 3F/8, so the answer is D.

In Frame 1, Two Identical Conducting Spheres, a and B