An electric dipole with dipole moment $\vec p$ is placed in a uniform electric field $\vec E$. The work done in rotating the dipole by $90^\circ$ from its initial equilibrium position is:

An electric dipole is formed by two charges $+q$ and $-q$ located in the $xy$-plane at $(0, 2) \text{ mm}$ and $(0, -2) \text{ mm}$,respectively,as shown in the figure. The electric potential at point $P(100, 100) \text{ mm}$ due to the dipole is $V_0$. The charges $+q$ and $-q$ are then moved to the points $(-1, 2) \text{ mm}$ and $(1, -2) \text{ mm}$,respectively. What is the value of the electric potential at $P$ due to the new dipole?

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

An electric dipole of dipole moment $6 \times 10^{-6} \ Cm$ is placed in a uniform electric field of magnitude $10^6 \ V/m$. Initially,the dipole moment is parallel to the electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field will be . . . . . . $J$.

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 $; eV.$)

$A$ dipole having dipole moment $p$ is placed in front of a solid uncharged conducting sphere as shown in the diagram. The net potential at point $A$ lying on the surface of the sphere is :-