An electric dipole of dipole moment $P$ is placed parallel to a uniform electric field of intensity $E$. On rotating it through an angle of $90^\circ$ from this position, the amount of work done is . . . . . . .

Two opposite and equal charges of $4 \times 10^{-8} \ C$ are placed at a distance of $2 \times 10^{-2} \ cm$ to form a dipole. If the dipole is placed in an external electric field of $4 \times 10^8 \ N/C$,calculate the maximum torque and the work done to rotate it by $180^{\circ}$.

Three point charges $+q$,$-2q$ and $+q$ are placed at points $(x = 0, y = a, z = 0)$,$(x = 0, y = 0, z = 0)$ and $(x = a, y = 0, z = 0)$ respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are

An electric dipole having dipole moment $P = q \times 2\ell$ is placed in a uniform electric field $E$. The dipole moment is along the direction of the field. The force acting on it and its potential energy are respectively

An electric dipole of moment $\overrightarrow{p} = (-\hat{i} - 3\hat{j} + 2\hat{k}) \times 10^{-29} \; C \cdot m$ is at the origin $(0, 0, 0)$. The electric field due to this dipole at $\overrightarrow{r} = \hat{i} + 3\hat{j} + 5\hat{k}$ (note that $\overrightarrow{r} \cdot \overrightarrow{p} = 0$) is parallel to

As shown in the figure,a charge $+q$ is moved from point $A \,(r, 135^{\circ})$ to point $B \,(r, 45^{\circ})$. If the dipole moment is $p$,what is the work done by an external agent?