Consider two charges $+q$ and $-q$ $(q > 0)$ placed at a distance $2a$ from each other. At the point $M$ (see figure below),the electric field makes an angle $\phi$ with the $x$-axis. The correct value of $\phi$ is (in $^{\circ}$)

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 $60^\circ$.

An electric dipole,when placed in a uniform electric field $E$,will have minimum potential energy when the angle made by the dipole moment with the field $E$ is

Three point charges $q, -2q$ and $q$ are placed along the $x$-axis at $x = -a, 0$ and $a$ respectively. As $a \rightarrow 0$ and $q \rightarrow \infty$ while $qa^2 = Q$ remains finite, the electric field at a point $P$, at a distance $x$ $(x \gg a)$ from $x = 0$ is $E = \frac{\alpha Q}{4 \pi \epsilon_0 x^\beta} \hat{i}$. Then:

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 . . . . . . .

An electric dipole with dipole moment $P$ and moment of inertia $I$ is placed in a uniform electric field of intensity $E$. If the dipole is slightly rotated,the angular frequency of its oscillation is ........