Three identical small electric dipoles are arranged parallel to each other at equal separation $a$ as shown in the figure. Their total interaction energy is $U$. Now,one of the end dipoles is gradually reversed. How much work is done by the electric forces?

$A$ positive charge $Q$ is distributed uniformly over a circular ring of radius $R$. $A$ point particle having a mass $m$ and a negative charge $-q$ is placed on its axis at a distance $x$ from the centre. Assuming $x \ll R$,find the time period of oscillation of the particle,if it is released from there [neglect gravity].

An electric dipole of length $4 \ cm$ is placed with its axis making an angle of $30^{\circ}$ with a uniform electric field of $10^6 \ N/C$. If it experiences a torque of $20 \sqrt{3} \ Nm$,then the potential energy of the dipole is $:-$ (in $J$)

An electric dipole is placed in an electric field generated by a point charge.

$A$ point dipole $\vec{p} = -p_0\hat{x}$ is kept at the origin. The potential and electric field due to this dipole on the $y$-axis at a distance $d$ are,respectively: (Take $V = 0$ at infinity)

An electric dipole with dipole moment $4 \times 10^{-14} \ C \cdot m$ is aligned at $30^{\circ}$ with the direction of a uniform electric field of magnitude $5 \times 10^4 \ N/C$. The magnitude of the torque acting on the dipole is: