Potential Energy of an Electric Dipole in a Uniform Electric Field

Two dipoles $p_1 \text{and} p_2$ are placed along the same axis at a distance $x$ apart as shown in figure. What is the magnitude of the force of interaction? What is the nature of force, attractive or repulsive?

A charge $+q$ is carried from a point $A\left(r, {135}^{°}\right)$ to $B\left(r, {45}^{°}\right)$ following a path, which is a quadrant of circle of radius $r$ (see figure). If the dipole moment is $P$, find the work done by the external agent (assume short dipole).

The potential energies associated with four orientations of an electric dipole in an electric field are $\left(1\right) -5U_0 , \left(2\right) -7U_0 , \left(3\right) 3U_0$ and $\left(4\right) 5U_0$ where $U_0$ is positive. Rank the orientations according to the

$\left(a\right)$ angle between the electric dipole moment $\overrightarrow{P}$ and the Electric field $\overrightarrow{E}$, and 

$\left(b\right)$ magnitude of the torque on the electric dipole, .

greatest first.

An electric dipole of length $4 \mathrm{cm}$, when placed with its axis making an angle of ${60}^{°}$ with a uniform electric field, experiences a torque of $4\sqrt{3} \mathrm{N} \mathrm{m}$. Calculate the

$\left(a\right)$ magnitude of the electric field , and

$\left(b\right)$ potential energy of the dipole,  if dipole has charges $\pm 8 \mathrm{nC}$.

A neutral water molecule $\left({\mathrm{H}}_2\mathrm{O}\right)$ in its vapour state has an electric dipole moment of magnitude $6.2\times {10}^{-30} \mathrm{C} \mathrm{m}$.

(a) If a molecule is placed in an electric field of $1.5\times {10}^4 \mathrm{N} {\mathrm{C}}^{-1}$, what is the maximum torque that the field can exert on it?

(b) How much work must an external agent do to turn this molecule end for end in this field starting from its fully aligned position for which $\theta =0°$?

The figure shows four orientations of an electric dipole in an external electric field.

$\left(a\right)$ If the dipole rotates from orientation $1$ to orientation $2$, is the work done on the dipole by the field positive, negative, or zero?

$\left(b\right)$ If the dipole rotates from orientation $1$ to orientation $4$, is the work done on the dipole by the field more than, less than, or the same as in $\left(a\right)$?

Figure shows four orientations of an electric dipole in an external electric field. Rank the orientations according to the

$\left(a\right)$ magnitude of the torque on the dipole, and 

$\left(b\right)$ potential energy of the dipole, greatest first.