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

When three electric dipoles are near each other,they each experience the electric field of the other two,and the three-dipole system has a certain potential energy. The figure below shows three arrangements $(1)$,$(2)$,and $(3)$ in which three electric dipoles are side by side. All three dipoles have the same magnitude of electric dipole moment,and the spacings between adjacent dipoles are identical. If $U_1$,$U_2$,and $U_3$ are potential energies of the arrangements $(1)$,$(2)$,and $(3)$ respectively,then:

$A$ dipole with two electric charges of $2 \ \mu C$ magnitude each,with separation distance $0.5 \ \mu m$,is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of $5 \ V$ is applied. Separation between the plates is $0.5 \ mm$. If the dipole is rotated by $30^{\circ}$ from the axis,it tends to realign in the direction due to a torque. The value of torque is $:$

An electric dipole is formed by placing a charge of $4 \times 10^{-8} \ C$ at a distance of $2 \times 10^{-2} \ cm$. If it is placed in an electric field of $4 \times 10^8 \ N/C$,what is the maximum torque acting on it and the work done to rotate the dipole by $180^{\circ}$?

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 $4 \,cm$.

An electric dipole has a charge of magnitude $q$ and a dipole moment $p$. It is placed in a uniform electric field $E$. If its dipole moment is aligned with the direction of the electric field, the force acting on it and its potential energy will be, respectively: