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 $J$)

Two charges $+3.2 \times 10^{-19} \, C$ and $-3.2 \times 10^{-19} \, C$ kept $2.4 \, \mathring{A}$ apart form a dipole. If it is kept in a uniform electric field of intensity $4 \times 10^5 \, V/m$,what will be its electrical potential energy in stable equilibrium?

Two charges $5 \text{ nC}$ and $-2 \text{ nC}$ are placed at points $(5 \text{ cm}, 0, 0)$ and $(23 \text{ cm}, 0, 0)$ in a region of space where there is no other external field. The electrostatic potential energy of this charge system is

Obtain the equation of electric potential energy of a dipole from the equation of potential energy of a system of two electric charges.

Derive the expression for the electric potential due to an electric dipole at a general point $P$ at a distance $r$ from its center.

Three charges $Q, +q$ and $+q$ are placed at the vertices of a right-angled isosceles triangle as shown in the figure. If the net electrostatic potential energy of the system is zero,the value of $Q$ is