The angle between the dipole moment and electric field at any point on the equatorial plane is (in $^{\circ}$)

If a dipole of dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$,then the torque acting on it is given by:

$A$ dipole with two electric charges of $2 \ \mu C$ magnitude each,with separation distance $0.5 \ \mu m$,is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of $5 \ V$ is applied. Separation between the plates is $0.5 \ mm$. If the dipole is rotated by $30^{\circ}$ from the axis,it tends to realign in the direction due to a torque. The value of torque is $:$

Two electric dipoles of moments $p$ and $27 p$ are placed in opposite directions on a line at a distance of $24 \,cm$. The electric field will be zero at a point between the dipoles whose distance from the dipole of moment $p$ is

The net electric field at the given point $O$ due to all the four identical short electric dipoles of dipole moment $p$ each,as shown in the figure,is $\left( k = \frac{1}{4\pi \varepsilon_0} \right)$.

An electric dipole of moment $\vec{p}$ is kept in a uniform electric field $\vec{E}$. The angle between $\vec{p}$ and $\vec{E}$ is $30^\circ$. Calculate the work done by the field when the angle is increased to $60^\circ$.