Three charges $Q, +q$ and $+q$ are placed at the vertices of a right -angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of $Q$ is

If $50$ joule of work must be done to move an electric charge of $2 \,C$ from a point, where potential is $-10$ volt to another point, where potential is $V$ volt, the value of $V$ is ......... $V$

A solid sphere of radius $R$ carries a charge $(Q+q)$ distributed uniformly over its volume. A very small point like piece of it of mass $m$ gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge $q.$ If it acquires a speed $v$ when it has fallen through a vertical height $y$ (see figure), then :

(assume the remaining portion to be spherical).

There exists an electric field of magnitude $E$ in $x$-direction. If the work done in moving a charge of $0.2 \,C$ through a distance of $2 \,m$ along a line making an angle $60^{\circ}$ with $x$-axis is $4 \,J$, then the value of $E$ is ........ $N / C$

If one of the two electrons of a $H _{2}$ molecule is removed, we get a hydrogen molecular ion $H _{2}^{+}$. In the ground state of an $H _{2}^{+}$, the two protons are separated by roughly $1.5\;\mathring A,$ and the electron is roughly $1 \;\mathring A$ from each proton. Determine the potential energy of the system. Specify your choice of the zero of potential energy.

The mean free path of electrons in a metal is $4 \times 10^{-8} \;m$. The electric field which can give on an average $2 \;eV$ energy to an electron in the metal will be in units of $V / m$