An electric dipole of dipole moment $\vec{P}$ is placed in a uniform electric field $\vec{E}$. Which of the following statements are correct?
Statement $I$: The torque on the dipole is $\vec{\tau} = \vec{P} \times \vec{E}$
Statement $II$: The potential energy of the dipole is $U = -\vec{P} \cdot \vec{E}$
Statement $III$: The net force on the dipole is non-zero

Two point dipoles of dipole moments $\vec{p}_1$ and $\vec{p}_2$ are at a distance $x$ from each other,and $\vec{p}_1 \parallel \vec{p}_2$. The force between the dipoles is:

An electric dipole of moment $\vec{P}$ is placed in a uniform electric field $\vec{E}$ such that $\vec{P}$ points along $\vec{E}$. If the dipole is slightly rotated about an axis perpendicular to the plane containing $\vec{E}$ and $\vec{P}$ and passing through the centre of the dipole, the dipole executes simple harmonic motion. Consider $I$ to be the moment of inertia of the dipole about the axis of rotation. What is the time period of such oscillation?

Two charges $+q$ and $-q$ are kept at a certain distance apart. Then, at any point on the right bisector of the line joining the two charges:

$A$ region surrounding a stationary electric dipole has:

The electric intensity due to a dipole of length $10 \, cm$ and having a charge of $500 \, \mu C$,at a point on the axis at a distance $20 \, cm$ from one of the charges in air,is