An electric dipole with dipole moment $4 \times 10^{-14} \ C \cdot m$ is aligned at $30^{\circ}$ with the direction of a uniform electric field of magnitude $5 \times 10^4 \ N/C$. The magnitude of the torque acting on the dipole is:

The force on a charge situated on the axis of a dipole is $F$. If the charge is shifted to double the distance,the new force will be

An electric dipole of length $20 \ cm$ having $\pm 3 \times 10^{-3} \ C$ charge is placed at $60^{\circ}$ with respect to a uniform electric field and experiences a torque of magnitude $6 \ N-m$. The potential energy of the dipole is:

The electric field due to a short electric dipole at a distance $r$ on the axial line from its mid-point is $x$ times the electric field at a distance $2r$ on the equatorial line from the mid-point of the dipole. Then,the value of $x$ is

$A$ charge is placed on the axis of an electric dipole and experiences a force $F$. If the distance is doubled,what will be the new force?

Charges $-q$ and $+q$ located at $A$ and $B$,respectively,constitute an electric dipole. Distance $AB = 2a$,$O$ is the midpoint of the dipole and $OP$ is perpendicular to $AB$. $A$ charge $Q$ is placed at $P$ where $OP = y$ and $y >> 2a$. The charge $Q$ experiences an electrostatic force $F$. If $Q$ is now moved along the equatorial line to $P'$ such that $OP' = \frac{y}{3}$,the force on $Q$ will be close to: $\left( \frac{y}{3} >> 2a \right)$