In the figure, curved lines represent equipotential surfaces. A charge \( Q \) is moved along different paths A, B, C, and D. The work done on the charge will be maximum along the path:
Show Hint
Remember that work done in moving a charge between equipotential surfaces is zero. The maximum work is done when the charge moves between the surfaces with the largest potential difference.
Work Done on a Charge Moving Along an Equipotential Surface
Moving a charge along an equipotential surface requires zero work. This is due to the zero potential difference between any two points on the same equipotential line. The work done in moving a charge \( Q \) between points with potentials \( V_1 \) and \( V_2 \) is defined as \( W = Q(V_2 - V_1) \). For an equipotential surface, \( V_1 = V_2 \), resulting in \( W = 0 \).
Maximum Work Done:
Observing the provided figure, the greatest potential difference is encountered when a charge moves between the 25V and 10V surfaces. Path D represents this scenario. Consequently, the maximum work is performed along path D due to the largest potential difference.
Conclusion:
Therefore, path D is identified as the correct answer, as it corresponds to the maximum potential difference and thus the maximum work done.
