The work done in moving a charge 'q' on an equipotential surface is. $\qquad$ ?

Appeared in: KPSC Staff Nurse - 2018

Explanation

An equipotential surface is defined as a surface where the electric potential is constant at every point.
The work done (W) in moving a charge (q) is the product of the charge and the potential difference (ΔV) between the start and end points: W = q × ΔV.
Since the charge moves along an equipotential surface, the starting potential and ending potential are the same, making the potential difference (ΔV) equal to zero.
Therefore, the work done is W = q × 0 = 0.

Option A: Work done is zero because there is no change in potential. Infinite work would imply an infinite potential difference, which is physically unrealistic in this context.
Option C: This value would only be correct if the charge 'q' were moved across a potential difference of 0.5 Volts. On an equipotential surface, the potential difference is zero.
Option D: This value would only be correct if the charge 'q' were moved across a potential difference of 2 Volts. On an equipotential surface, the potential difference is zero.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work Done on an Equipotential Surface as background academic context rather than a clinical decision trigger.
While this is a physics concept, the principle of electric potential difference is fundamental to medical diagnostics like Electrocardiography (ECG) and Electroencephalography (EEG), which measure potential differences on the body's surface generated by the heart and brain, respectively.
Understanding potential difference is also crucial for procedures involving electricity, such as defibrillation and pacemakers.
What if? If the charge 'q' were moved from an equipotential surface of 10V to another of 5V, the work done would not be zero. It would be W = q × (5V - 10V) = -5q Joules. The negative sign indicates that the electric field does the work, and the charge loses potential energy.

How to Approach the Question

First, identify the key terms in the question: 'work done' and 'equipotential surface'.
Recall the definition of an 'equipotential surface'. It is a surface where the electric potential (V) is the same at every point.
Next, recall the formula for the work done (W) in moving a charge (q) through a potential difference (ΔV): W = q × ΔV.
Connect the definition to the formula. Since the charge is moving on an equipotential surface, the initial potential (V_initial) is equal to the final potential (V_final).
Calculate the potential difference: ΔV = V_final - V_initial = 0.
Substitute this value into the work formula: W = q × 0 = 0.

Concept Tested & Keywords

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Practise the full KPSC Staff Nurse - 2018

Attempt every question from this paper in a timed mock, then review the full solution for each one.