$($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 $-Q_0.$ 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.

$P$

$($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 $+Q_p$ 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.