UPPSC PCS - 2021

With reference to the electric potential, which of the following statements is/are correct ? 1). It is a scalar quantity. 2). It is a vector quantity. Select the correct answer using the codes given below. Codes:

Year Asked: 2021

A
Only 1
B
Only 2
C
Both 1 and 2
D
Neither 1 nor 2

Correct Answer

A. Only 1

Detailed Explanation

Electric potential at a point is the work done per unit positive charge in bringing a test charge from infinity to that point against the electrostatic force. Work is a scalar, so potential is a scalar. Statement 1 is correct and statement 2 is wrong, so option A is the answer.

  • Statement 1: correct. Potential has only magnitude and sign, and its SI unit is the volt (1 V = 1 J/C).
  • Statement 2: incorrect. A vector needs direction as well as magnitude. Electric field intensity E is the vector quantity, and it equals the negative gradient of potential, E = -dV/dr. Potentials from several charges add algebraically, not by vector addition.
  • Options B, C and D: all rejected because statement 2 is false.

Core concept: the difference between potential (scalar, energy per unit charge) and field (vector, force per unit charge). This connects to Physics in the Prelims syllabus and to Mains questions on capacitors, equipotential surfaces, and why the field at a conductor surface is perpendicular to that surface.

Trap: students remember that field and potential are related and then mark both statements as correct, or choose option C. The link between them is a gradient, and only the field is a vector.

This question appeared in UPPCS 2021 General Studies Paper I.

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