An electric dipole of length $4 \ cm$ is placed with its axis making an angle of $60^{\circ}$ with a uniform electric field. It experiences a torque of $4 \sqrt{3} \ Nm$. Calculate the magnitude of the electric field. (The dipole has charges $\pm 8 \ nC$)

Three point charges of $+2q, +2q$ and $-4q$ are placed at the corners $A, B$ and $C$ of an equilateral triangle $ABC$ of side '$x$'. The magnitude of the electric dipole moment of this system is

An electric dipole is placed along the $x$-axis at the origin $O$. $A$ point $P$ is at a distance of $20 \, cm$ from this origin such that $OP$ makes an angle $\frac{\pi}{3}$ with the $x$-axis. If the electric field at $P$ makes an angle $\theta$ with the $x$-axis,the value of $\theta$ would be

An electric dipole with dipole moment $5 \times 10^{-7} \text{ C m}$ is placed in an electric field of $2 \times 10^4 \text{ N C}^{-1}$ at an angle of $60^{\circ}$ with the direction of the electric field. The torque acting on the dipole is:

The electric dipole is situated in an electric field as shown in figure $(i)$. The dipole and electric field are both in the plane of the paper. The dipole is rotated about an axis perpendicular to the paper at point $A$ in an anticlockwise direction. If the angle of rotation is measured with respect to the direction of the electric field,then the torque for different values of the angle of rotation $\theta$ will be as represented in Fig. $(ii)$.

The dipole moment of a system of charge $+q$ distributed uniformly on an arc of radius $R$ subtending an angle $\pi /2$ at its centre, where another charge $-q$ is placed at the centre, is: