Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(d, 0)$ respectively of an $x-y$ coordinate system. Then:

The electric field and the potential of an electric dipole vary with distance $r$ as

An electric dipole of moment $p$ is placed at the origin along the $x$-axis. The electric field at a point $P$,whose position vector makes an angle $\theta$ with the $x$-axis,will make an angle $\phi$ with the $x$-axis. If $\tan \alpha = \frac{1}{2} \tan \theta$,where $\alpha$ is the angle between the electric field vector and the position vector,then the angle $\phi$ that the electric field makes with the $x$-axis is:

An electric dipole moment $\vec{p} = (2.0\hat{i} + 3.0\hat{j}) \times 10^{-6} \text{ C m}$ is placed in a uniform electric field $\vec{E} = (3.0\hat{i} + 2.0\hat{k}) \times 10^{5} \text{ N C}^{-1}$. Which of the following statements is correct?

An electric dipole is placed along the $x$-axis with its center at the origin. The line $OP$ makes an angle of $\frac{\pi}{3}$ with the $x$-axis. If the electric field at point $P$ makes an angle $\theta$ with the $x$-axis,then $\theta$ is equal to:

An electric dipole of length $2 \ cm$ is placed with its axis making an angle of $60^{\circ}$ to a uniform electric field of $10^{5} \ N/C$. If it experiences a torque of $8 \sqrt{3} \ Nm$,calculate the magnitude of the charge on the dipole. (Given: $\sin 60^{\circ} = \frac{\sqrt{3}}{2}$)