Question

Define electric potential energy, electric potential, and equipotential surfaces?

Can equipotential surfaces touch or cross one another? If yes/no, why/how?

Under what angle do the electric field lines cross equipotential surfaces?

Explain why, if all charges are at rest, the surface of a conductor is an equipotential surface?

What’s the relationship between the electric potential on the surface of and inside the conductor when all charges are at rest?

Define electron volt.

If you know electric potential V as a function of coordinates (x, y, z), how would you calculate the electric field vector?

Answer 1

1) Electric potential energy is a potential energy (measured in joules) that results from conservative Coulomb forces and it is defined as the product of the charges and the electric potential.

The electric potential is the amount of work needed to move a unit positive charge from a reference point to a specific point inside the field without producing any acceleration. The electric potential due to a point charge Q is defined as

Equipotential surfaces are the surfaces with same electric potential at every point.

on an equipotential surface.

2) Two equipotential lines cannot cross each other because, at the point of intersection, there will be two values of potential at the same point, which is not possible.

3) The electric field makes 90 degrees when it crosses equipotential surfaces. Or in other words, electric field lines are perpendicular to equipotential surfaces.

4) Since all the charges are at rest, the electric field's tangential component just outside the surface is zero. If it were not, a charge could move in a rectangular path partly inside the conductor and partly outside the conductor and return to its initial position with a net amount of work done. But this would violate the conservative nature of electrostatic force. Hence the electric field is perpendicular to the surface of the conductor. Which means the surface of a conductor is an equipotential surface.

5) Since the electric field inside a conductor is zero and potential is a gradient of the field, it remains constant inside the conductor. This constant value is the same as the potential on the surface of the conductor.

6) An electron volt is defined as the work done on an electron in accelerating it through a potential difference of one volt.

7) The electric field is the negative gradient of the potential. Hence the electric field vector is