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
The work done on a charge when it moves along an equipotential surface is zero. This is because the potential difference between any two points on the same equipotential surface is zero. To understand this concept, let's look at the work done when moving a charge in the presence of a potential difference.
Work Done on a Charge:
The work done \( W \) when moving a charge \( Q \) between two points with potential difference \( V_1 \) and \( V_2 \) is given by:
\[ W = Q(V_2 - V_1) \]
For any path along an equipotential surface, \( V_1 = V_2 \), meaning there is no potential difference, and therefore the work done \( W \) is zero.
Maximum Work Done:
From the given figure, the maximum potential difference occurs when the charge moves from the 25V surface to the 10V surface. The path corresponding to this maximum potential difference is along path D. Since the potential difference is the largest between these two surfaces, the maximum work done will be along this path.
Conclusion:
Thus, the correct answer is path D, as this gives the maximum potential difference and the maximum work done.
