Question

The diagrams below show regions of equipotentials.

A positive charge is moved from A to B in each diagram.

• A. Maximum work is required to move q in figure (c).
• B. In all the four cases the work done is the same.
• C. Minimum work is required to move q in figure (a).
• D. Maximum work is required to move q in figure (b).

Answer 1

The Correct Option is B

To understand the work done in moving a positive charge from point A to point B across equipotentials, we should recall that:

• The work done W in moving a charge q between two points of different potentials is given by the equation: W = q \cdot (V_{\text{final}} - V_{\text{initial}}).
• If the points are on the same equipotential line, the potential difference (V_{\text{final}} - V_{\text{initial}}) is zero, hence no work is done.

In the diagrams provided:

Considering each scenario:

1. Figure (a): The charge moves from 20 V to 40 V.
2. Figure (b): The charge moves from 20 V to 40 V.
3. Figure (c): The charge moves from 20 V to 40 V.
4. Figure (d): The charge moves from 20 V to 40 V.

In all cases, the potential difference is 20 V (from 20 V to 40 V). Therefore, the work done in terms of charge q is identical:

• W = q \cdot (40\,\text{V} - 20\,\text{V}) = q \cdot 20\,\text{V}

So, the correct option is: In all the four cases the work done is the same.