The electric potential at a point on the axis of an electric dipole depends on the distance $r$ of the point from the dipole as

Two charges of $-4 \ \mu C$ and $+4 \ \mu C$ are placed at the points $A(1, 0, 4) \ m$ and $B(2, -1, 5) \ m$ located in an electric field $\vec{E} = 0.20 \ \hat{i} \ V/cm$. The magnitude of the torque acting on the dipole is $8 \sqrt{\alpha} \times 10^{-5} \ Nm$. Where $\alpha = $ . . . . . .

Write the equation for the electric field produced by an electric dipole at a point on its equatorial line,given the condition $r >> a$ (where $r$ is the distance from the center and $2a$ is the dipole length).

Two point masses,each of mass $m$ and charges $+q$ and $-q$,are attached to the ends of a massless rod of length $L$. This assembly is placed in a uniform electric field of intensity $E$ at a small angle $\theta$ with the field. How much time will it take for the rod to become parallel to the electric field?

An electric dipole is placed at a distance of $2 \ cm$ from an infinite plane sheet having positive charge density $\sigma_0$. Choose the correct option from the following.

In a certain region of space,the electric field is along the $z$-direction throughout. The magnitude of the electric field is,however,not constant but increases uniformly along the positive $z$-direction at the rate of $10^{5} \; N \, C^{-1}$ per meter. What are the force and torque experienced by a system having a total dipole moment equal to $10^{-7} \; C \, m$ in the negative $z$-direction?