2. (12 points, suggested time 25 minutes) Pivot. Rod. m, +20 Figure 1 m, +20 Note: Figure 1 not drawn to scale. ト Figure 2 Figure 3 Two insulating spheres with mass m and charge +Q, are near Earth's surface, suspended vertically from identical light, stiff rods with pivots at the top, as shown in Figure 1. The spheres are initially far apart. The pivots are locked so the rods remain vertical while the spheres are moved together by external forces until the spheres are a distance, from each other, as shown in Figure 2. Finally, the pivots are held a distance 72 apart and unlocked, and the rods are allowed to swing out until the spheres momentarily come to a rest a distance 7; apart, as shown in Figure 3. The pivots are always at the same height. (a) Consider the system that includes only the two spheres, with Earth external to the system. (i) Write an expression for the work done moving the spheres horizontally from far apart to a separation of 72. Express your answer in terms of Q.12, and physical constants, as appropriate. (11) The total energy of the two-sphere system (with Earth still external to the system) changes as the system goes from the configuration in Figure 2 to the configuration in Figure 3. Explain how the energy changes in terms of the forces exerted on the system. (b) Now consider the system that contains both Earth and the two spheres. What is the work done on this new system for the changes in sphere position described in parts (a)(i) and (ii)? Explain your reasoning. Part (a)(i) Part (a)(ii) (c) The rods are now held fixed at the positions shown in Figure 3, and negative charge is added to the right sphere so its net charge is - Q. The circles in the figure below represent the spheres. On the figure, do the following. • Draw a single vector originating on point P that represents the net electric field at that point. ⚫ For each of the dots on the horizontal dashed line, draw an isoline of electric potential that goes through the dot. •P --(+20) (-20)- (d) In a new situation, the two spheres still have the same mass m, but the left sphere is made of plastic and has charge +Q, and the right sphere is made of metal and is uncharged. The spheres are brought near but do not touch, as shown below on the left. When the rods are allowed to pivot, the spheres move toward each other, as shown on the right. In terms of charge distributions, explain why the force between the spheres is attractive. Plastic m, +Qp Metal m, Uncharged