Question

The amount of work done in moving a unit positive charge through a distance of $10{\text{ }}cm$ on an equipotential surface is ?

Answer 1

Remember the concept of equipotential surface, an equipotential surface is defined as a surface with the same potential at its every point. Thus we can get some idea of Work done from this as we know that the formula of work done is $W = {\text{Q}} \times \Delta {\text{V}}$.

Complete step by step answer:
To solve the question, we need to have the required values of $Q$ charge = $1$ unit positive charge, and the value of Potential difference ( $10{\text{ }}cm$ apart points) $\Delta V$, but from the question we learn that the surface is Equipotential, and thus each point is at same potential, thus $\Delta V$ = 0. Hence by the definition of work:
$W = {\text{Q}} \times \Delta {\text{V}}\\\ \Rightarrow W=1 \times 0 \\\ \therefore W=0{\text{ J}}$
Thus the amount of work done in moving a unit positive charge through a distance of $10{\text{ }}cm$ on an equipotential surface is ZERO. Note that we do not consider directions in case of calculating work due to Potential differences.

Additional Information: The electric field is always perpendicular to the equipotential surface, hence two equipotential surfaces will never intersect. Thus, from this we generate a concept that in a uniform electric field any plane normal to it is always an equipotential surface. For a point charge remember that the equipotential surface is a concentric electric sphere.

Note: The main thing is that the concept of work done and potential difference should be remembered. If you know all the basic concepts of Static electricity , then these questions will be easy to solve. Another formula which is to be kept in mind is $F = {\text{ Q}} \times {\text{E}}$.