Metal sphere A is charged negatively and then brought near an uncharged metal sphere B (Figure 14.78). Both spheres rest on insulating supports, and the humidity is very low.

(a) Use +’s and −’s to show the approximate distribution of charges on the two spheres. (Hint: Think hard about both spheres, not just B.)

(b) A small, lightweight hollow metal ball, initially uncharged, is suspended from a string and hung between the two spheres (Figure 14.79). It is observed that the ball swings rapidly back and forth hitting one sphere and then the other. This goes on for seconds, but then the ball stops swinging and hangs between the two spheres. Explain in detail, step by step, why the ball swings back and forth and why it finally stops swinging. Your explanation must include good physics diagrams.

The given data can be listed below as follows,

• The metal sphere A is negatively charged.
• The metal sphere B is uncharged.
• The ball has swung for $5s$.

Charging by induction illustrates that an uncharged particle gets charged if it is kept beside the charged particle.

Also, induction charging is described as a process in which an object can be changed without touching it.

The induction charging gives the charge distribution of the spheres and why the ball moved back and forth.

(a)

According to the law of induction, the charged sphere distributes charge to the uncharged sphere until both the spheres get an equal charge. Hence, both the spheres get an equal amount of negative charge due to the charging by induction.

As sphere A is negatively charged and sphere B is uncharged, the charge will flow from sphere A to sphere B according to the induction charging. The charge flowing will continue until both the spheres’ charge remains equal.

Thus, sphere B will get about amount of negative charge, and sphere A will have about amount of negative charge.

(b)

The diagram of the spheres has been drawn below,

The above diagrams have shown how the lightweight hollow metal ball is swinging back and forth and stops eventually. Here, in figure 1, when the charge of the sphere A is going towards the sphere B, the ball is also moving and goes towards the sphere B as it was also uncharged. Moreover, according to Newton’s third law, sphere B exerts an equal and opposite force on sphere A which causes the ball to move to sphere A which is shown in figure 2. Hence, in figure 1 and figure 2, the ball moves due to the charge distribution between the spheres.

Finally, in figure 3, when both the spheres become equally charged, there is no charge distribution, and the ball hangs still. Hence, the ball is swinging back and forth because of the unequal distribution of charges, and when the distribution of the charges becomes equal, the ball stops swinging. Hence, in figure 3, as the charge distribution between the spheres stopped, the ball stopped moving.

Thus, due to the charge distribution from sphere A to sphere B, the ball is moving towards sphere B, and as sphere B is producing an equal and opposite force on sphere A, the ball is moving to sphere A with this. Finally, when both spheres have equal charge, the ball stops moving as there is no unequal charge.