If a unit positive charge is taken from one point to another over an equipotential surface then

Question

Accepted Answer

The correct option is (4): No work is done.

An equipotential surface is defined as a surface where the electric potential is the same at every point. This means that if you take any two points, say A and B, on an equipotential surface, the potential difference between them, $V_B - V_A$, is zero.

The work done ($W$) in moving a charge ($q$) from one point to another in an electric field is given by the formula:
$W = q (V\_B - V\_A)$

Since, for an equipotential surface, $V\_B - V\_A = 0$, substituting this into the work done formula gives:
$W = q 	imes 0$
$W = 0$

Therefore, no work is done by or on the electric field when a charge is moved from one point to another on an equipotential surface. This is a fundamental concept in electrostatics. It implies that the electric field lines are always perpendicular to the equipotential surfaces, as any component of the electric field along the surface would result in work being done.

The incorrect option is (1): Work is done on the charge.
This is incorrect because for work to be done on the charge, there must be a potential difference between the initial and final points, which is not the case on an equipotential surface.

The incorrect option is (2): Work is done by the charge.
This is incorrect for the same reason as option (1). If there is no potential difference, no work can be done by the charge (or the field).

The incorrect option is (3): Work done is constant.
While the work done is a constant value (zero) in this specific scenario, the statement "Work done is constant" itself doesn't fully capture the essence that the constant value is specifically zero due to the nature of an equipotential surface. It's not just "constant" but "constantly zero."