An electric dipole of length $4 \ cm$ is placed with its axis making an angle of $30^{\circ}$ with a uniform electric field of $10^6 \ N/C$. If it experiences a torque of $20 \sqrt{3} \ Nm$,then the potential energy of the dipole is $:-$ (in $J$)

Two charges each of magnitude $0.01\,C$ and separated by a distance of $0.4\,mm$ constitute an electric dipole. If the dipole is placed in a uniform electric field $\vec{E}$ of $10\,dyne/C$ making a $30^{\circ}$ angle with $\vec{E}$,the magnitude of torque acting on the dipole is:

An electron and a proton are at a distance of $1\,\mathring{A}$. The dipole moment of this system will be in $(C \cdot m)$:

If ${E_a}$ is the electric field strength of a short dipole at a point on its axial line and ${E_e}$ is the electric field strength on the equatorial line at the same distance,then:

$A$ given charge situated at a distance $r$ from an electric dipole on its axis experiences a force $F$. If the distance of the charge from the dipole is doubled,the force acting on the charge will be

An electric dipole with dipole moment $2 \times 10^{-10} \text{ C m}$ is aligned at an angle $30^{\circ}$ with the direction of a uniform electric field of $10^4 \text{ N C}^{-1}$. The magnitude of the torque acting on the dipole is: