Consider the configuration of a system of four charges each of value $+q$. Find the work done by external agent in changing the configuration of the system from figure $\left(\mathrm{i}\right)$ to figure. $\left(\mathrm{ii}\right)$.

 

If the charge on plate$1$ be $+q$, then the charges on the plates $2,3,4$ and $5$ are

When a negatively charged rod is brought near, but does not touch, the initially uncharged electroscope shown below, the leaves spring apart (I). When the electroscope is then touched with a finger, the leaves collapse (II). When next the finger and finally the rod are removed, the leaves spring apart a second time (III). The charge on the leaves is

Two small insulating spheres are attached to silk threads. The spheres have equal masses of $40 \mathrm{g}$ and have electric charges of $q_1=+2.0 \mu \mathrm{C}$ and $q_2=-2.0 \mu \mathrm{C}$. The spheres are brought into the initial positions shown in Figure (a), with a vertical separation of $15 \mathrm{cm}$ between them. In figure, the upper thread is slowly pulled upward, while point $B$ is kept fixed. When point $A$ has been raised through a height $h$, the lower sphere suddenly falls, as shown in Figure (b). The height $h$, is closest to:

          (a)                 (b)