Three identical small electric dipoles are arranged parallel to each other at equal separation a as shown in the figure. Their total interaction energy is $U$. Now one of the end dipole is gradually reversed, how much work is done by the electric forces.

$(a)$ Calculate the potential at a point $P$ due to a charge of $4 \times 10^{-7}\; C$ located $9 \;cm$ away.

$(b)$ Hence obtain the work done in bringing a charge of $2 \times 10^{-9} \;C$ from infinity to the point $P$. Does the answer depend on the path along which the charge is brought?

Figure shows a solid metal sphere of radius $‘a’$ surrounded by a concentric thin metal shell of radius $2a$ . Initially both are having charges $Q$ each. When the two are connected by a conducting wire as shown in the figure, then amount of heat produced in this process will be 

A point charge $q$ of mass $m$ is suspended vertically by a string of length $l$. A point dipole of dipole moment $\overrightarrow{ p }$ is now brought towards $q$ from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole, the angles and distances is shown in the figure below. If the work done in bringing the dipole to this position is $N \times( mgh )$, where $g$ is the acceleration due to gravity, then the value of $N$ is. . . . . . (Note that for three coplanar forces keeping a point mass in equilibrium, $\frac{F}{\sin \theta}$ is the same for all forces, where $F$ is any one of the forces and $\theta$ is the angle between the other two forces)

When one electron is taken towards the other electron, then the electric potential energy of the system

The escape speed of an electron launched from the surface of a glass sphere of diameter $1\ cm$ that has been charged to $10\ nC$ is $x \times 10^7\ m/sec$ . The value of $x$ is