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

The distance between $H^+$ and $Cl^-$ ions in an $HCl$ molecule is $1.28 \, \mathring{A}$. What will be the electric potential due to this dipole at a distance of $12 \, \mathring{A}$ on the axis of the dipole (in $, V$)?

An electric dipole is as shown in the figure. The electric potential at point $P$ due to the dipole is $[\epsilon_0 = \text{permittivity of free space}]$.

$A$ moving positive charge approaches a negative charge. What will happen to the potential energy of the system?

When a dipole placed parallel to electric field is rotated through $\pi^c$, the work done is $W$. The work done in rotating the dipole through $(\frac{\pi}{3})^c$ is $(\cos 0^\circ = 1, \cos 60^\circ = \frac{1}{2}, \cos 180^\circ = -1)$

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 $1.5 \; Å,$ and the electron is roughly $1 \; Å$ from each proton. Determine the potential energy of the system. Specify your choice of the zero of potential energy. (in $; eV.$)