Question

What is an equipotential surface? Show that no work is done in moving a given charge over an equipotential surface.

Hint:

Work done is the product of charge and potential difference. Since the potential difference is zero on an equipotential surface, the work done is zero.

Answer 1

Step 1: Definition of equipotential surface.
An equipotential surface is a surface on which the electric potential at every point is the same. In other words, no matter where you move a point on the surface, the potential remains constant. These surfaces are perpendicular to the electric field lines at every point.
For example, in a uniform electric field, the equipotential surfaces are planes that are parallel to each other and perpendicular to the field lines. In a point charge field, the equipotential surfaces are spheres centered at the point charge. Step 2: Work done in moving a charge over an equipotential surface.
The work \( W \) done in moving a charge \( q \) through a potential difference \( V \) is given by the equation: \[ W = q \cdot V \] where: - \( W \) is the work done, - \( q \) is the charge, - \( V \) is the potential difference.
Since the potential difference \( V \) between any two points on an equipotential surface is zero (because the potential is the same everywhere on the surface), the work done in moving a charge over an equipotential surface is: \[ W = q \cdot 0 = 0 \] Step 3: Conclusion.
Thus, no work is done in moving a given charge over an equipotential surface, as there is no potential difference between any two points on the surface.