Electrostatics

The electrostatic force between two charges is given by Coulomb's law: If the charges are halved, , and the distance is doubled, , then the new force is:

In a uniform electric field, a dipole experiences a torque but no net translational force, because the forces on the positive and negative charges cancel out.
In a non-uniform electric field, the magnitudes of forces on each charge differ due to the field's variation.
Thus, the dipole experiences: - Torque: due to opposite forces trying to align it with the field, - Net Force: due to unequal forces on and ends of the dipole.
Hence, both force and torque act on the dipole.

For a hollow spherical shell (conducting), the electric potential inside the shell (i.
e.
, for ) is constant and equal to the potential at the surface.
For , the shell behaves like a point charge at the center, and potential decreases as: Thus, the correct graph is constant from the center to the surface, then falling as .

By Gauss's law, total electric flux through a closed surface enclosing a charge is: If the charge is placed at the center of a cube, the flux will distribute equally through all 6 faces of the cube.
So, flux through one face: Since charge is given in microcoulombs ( ), the flux becomes: But the question directly gives charge in microcoulombs and expects answer in terms of , so Carefully matching units, the correct answer is: