In the situation shown in the diagram, magnitude, if $$q < < |Q|$$ and $$r >>>a$$. The net force on the free charge $$-q$$ and net torque on it about $$O$$ at the instant shown are respectively.

($$p=2 a Q$$ is the dipole moment)

A uniform electric field vector $$\mathbf{E}$$ exists along horizontal direction as shown. The electric potential at $$A$$ is $$V_A$$. A small point charge $$q$$ is slowly taken from $$A$$ to $$B$$ along the curved path as shown. The potential energy of the charge when it is at point $$B$$ is

A cubical Gaussian surface has side of length $$a=10 \mathrm{~cm}$$. Electric field lines are parallel to $$X$$-axis as shown in figure. The magnitudes of electric fields through surfaces $$A B C D$$ and $$E F G H$$ are $$6 ~\mathrm{kNC}^{-1}$$ and $$9 \mathrm{~kNC}^{-1}$$ respectively. Then, the total charge enclosed by the cube is

[Take, $$\varepsilon_0=9 \times 10^{-12} \mathrm{~Fm}^{-1}$$ ]

Electric field at a distance $$r$$ from an infinitely long uniformly charged straight conductor, having linear charge density $$\lambda$$ is $$E_1$$. Another uniformly charged conductor having same linear charge density $$\lambda$$ is bent into a semicircle of radius $$r$$. The electric field at its centre is $$E_2$$. Then