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

An electric dipole is placed at an angle $60^{\circ}$ with an electric field of strength $4 \times 10^5 \,N/C$. It experiences a torque equal to $8 \sqrt{3} \,Nm$. Calculate the charge on the dipole,if the dipole length is $4 \,cm$.

Two point dipoles $p \hat{k}$ and $\frac{p}{2} \hat{k}$ are located at $(0, 0, 0)$ and $(1 \text{ m}, 0, 2 \text{ m})$ respectively. The resultant electric field due to the two dipoles at the point $(1 \text{ m}, 0, 0)$ is

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 $\pm 8 \ nC$)

An electric dipole of mass $m$,charge $q$,and length $l$ is placed in a uniform electric field $\vec{E} = E_0 \hat{i}$. When the dipole is rotated slightly from its equilibrium position and released,the time period of its oscillations will be:

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