$A$ molecule of a substance has a permanent dipole moment $p$. $A$ mole of this substance is polarized by applying a strong electrostatic field $E$. The direction of the field is suddenly changed by an angle of $60^{\circ}$. If $N$ is the Avogadro's number,the amount of work done by the field is:

The electric potential in volts due to an electric dipole of dipole moment $2 \times 10^{-8} \, C \cdot m$ at a distance of $3 \, m$ on a line making an angle of $60^{\circ}$ with the axis of the dipole is ..........

Three point charges $1 \text{ C}, 2 \text{ C}$ and $3 \text{ C}$ are placed at the corners of an equilateral triangle of side $1 \text{ m}$. The work done to move these charges to the corners of another equilateral triangle of side $0.5 \text{ m}$ is

An electric dipole with dipole moment $\vec{p}_i = (3\hat{i} + 4\hat{j}) \times 10^{-30} \, \text{C-m}$ is placed in an electric field $\vec{E} = 4000 \hat{i} \, \text{N/C}$. An external agent turns the dipole slowly until its electric dipole moment becomes $\vec{p}_f = (-4\hat{i} + 3\hat{j}) \times 10^{-30} \, \text{C-m}$. The work done by the external agent is equal to:

Three charges $Q$,$(-2q)$ and $(-2q)$ are placed at the vertices of an isosceles right-angled triangle as shown in the figure. The net electrostatic potential energy is zero if $Q$ is equal to

Three point charges $3 \text{ nC}$,$6 \text{ nC}$,and $9 \text{ nC}$ are placed at the corners of an equilateral triangle of side $0.1 \text{ m}$. The potential energy of the system is: