Explanation:

When an electron moves from one point to another on an equipotential surface, the potential difference between the two points is zero. This means that the electric field between the two points is zero, and therefore no work is done in moving the electron.

Equipotential Surfaces:

Equipotential surfaces are imaginary surfaces in an electric field where the potential at every point on the surface is the same. These surfaces are always perpendicular to the electric field lines. The potential difference between any two points on an equipotential surface is zero.

Work Done:

Work done is defined as the product of force and displacement. In the case of moving an electron, the force acting on the electron is given by the electric field. If the electron is moving along an equipotential surface, the electric field between the two points is zero. Therefore, the force on the electron is zero, and hence no work is done in moving the electron.

Mathematical Explanation:

The work done in moving a charged particle in an electric field is given by the equation W = q * V, where W is the work done, q is the charge of the particle, and V is the potential difference.

In this case, the electron has a charge of -1.6 x 10^-19 Coulombs, and the potential difference between the two points on the equipotential surface is 10 Volts. Therefore, the work done can be calculated as:

W = (-1.6 x 10^-19 C) * (10 V)
= -1.6 x 10^-18 J

Since the work done is negative, it means that work is done by an external force to move the electron against the electric field. However, in the case of an equipotential surface, the potential difference is zero, and therefore the work done is zero.

Conclusion:

In conclusion, the work done in moving an electron from one point to another on an equipotential surface is zero. This is because the potential difference between the two points is zero, and therefore the electric field between the points is zero. As a result, no force acts on the electron, and hence no work is done in moving it.