Two charges $10 \mu C$ and $-10 \mu C$ are placed at points $A$ and $B$ separated by a distance of $10 \ cm$. Find the electric field at a point $P$ on the perpendicular bisector of $AB$,at a distance of $12 \ cm$ from its midpoint.

Electric field at the equator of a dipole is $E$. If both dipole moment and distance are doubled,then the electric field will be $:-$

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 $J$)

$A$ molecule of a substance has a permanent electric dipole moment of magnitude $10^{-29} \text{ C m}$. $2 \text{ mole}$ of this substance is polarized (at low temperature) by applying a strong electrostatic field of magnitude $10^6 \text{ V m}^{-1}$. What is the potential energy of the system? ($1 \text{ mole}$ of substance contains $6 \times 10^{23}$ molecules.)

An electric dipole having each charge of magnitude $2 \mu C$ is placed in an electric field of intensity $8 \times 10^{4} \ N/C$. If the maximum torque acting on the dipole is $4 \times 10^{-3} \ N \cdot m$,the length of the dipole is: (in $mm$)

An electric dipole with dipole moment $p$ is placed with its axis at $30^{\circ}$ to a uniform electric field. The work done in rotating the dipole to a position where its axis is perpendicular to the field is