Three point charges $+q$, $+2q$, and $+Q$ are placed at the three vertices of an equilateral triangle. If the potential energy of the system of three charges is zero, the value of $Q$ in terms of $q$ is

In bringing an electron towards another electron,the electrostatic potential energy of the system

Two opposite and equal charges each of magnitude $4 \times 10^{-8} \text{ C}$ form a dipole. Their separation is $2 \times 10^{-2} \text{ cm}$. When this dipole is placed in an external electric field of $4 \times 10^8 \text{ NC}^{-1}$,the value of maximum torque and the work done in rotating it through $180^{\circ}$ respectively will be:

Two equal charges of magnitude $Q$ each are placed at a distance $d$ apart. Their electrostatic energy is $E$. $A$ third charge $-Q / 2$ is brought midway between these two charges. The electrostatic energy of the system is now

The charges $+q$,$+q$,and $Q$ are placed at the vertices of an equilateral triangle of side $a$. If the net electrostatic potential energy of the system is zero,then $Q$ is equal to:

Two positive point charges of $10 \ \mu C$ and $12 \ \mu C$ are placed $10 \ cm$ apart in air. The work done to bring them $6 \ cm$ closer is (in $J$)