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.
- (a)Only 1
- (b)Only 2
- (c)Both 1 and 2
- (d)Neither 1 nor 2
Correct — A, Only 1. Electric potential (V) at a point is defined as the work done per unit positive charge in bringing a test charge from infinity to that point. It has magnitude (measured in volts) but no direction, so it is a SCALAR quantity — statement 1 is correct. It is not a vector, so statement 2 is wrong. (The associated vector quantity is the electric field E, which does have direction.) Hence only statement 1 is correct.
- (b)Only 2 — Wrong — electric potential is not a vector; it is completely specified by magnitude alone (volts), so statement 2 is false.
- (c)Both 1 and 2 — Wrong — a quantity cannot be both scalar and vector; potential is scalar, so statement 2 fails.
- (d)Neither 1 nor 2 — Wrong — statement 1 is correct: electric potential is indeed a scalar quantity.
Electric potential V is the electric potential energy per unit charge (V = W/q), measured in volts (joules per coulomb). Because it is specified fully by magnitude — with no direction — it is a scalar. It must not be confused with the electric field E, a vector (magnitude and direction) related to potential by E = −dV/dr, the negative gradient of potential. Potential difference (voltage) is likewise a scalar.
The trap is that electricity 'feels' directional, tempting statement 2. But direction belongs to the electric field, not the potential. Test the definition: potential is energy-per-charge (a number of volts), which has no direction → scalar → only statement 1 holds → answer (a).
- Electric potential V = work done per unit charge; SI unit is the volt (V = J/C).
- It is a scalar quantity — magnitude only, no direction.
- The electric field E is the related vector quantity (E = −gradient of V).
- Other scalars: energy, work, pressure, speed; other vectors: force, velocity, momentum, electric field.
Electric potential is a scalar; the electric field is its associated vector (E = −dV/dr).
- Assuming anything 'electric' is directional/vector — potential is scalar; only the field is a vector
- Confusing electric potential (scalar) with electric field (vector)
UPSC & UPPSC test scalar/vector classification directly ('which is a vector/scalar?') or, as here, by asserting a quantity's nature and asking you to judge it.
Which one of the following is a vector quantity?
- (a) Momentum
- (b) Pressure
- (c) Energy
- (d) Work
Answer(a) Momentum
Tests the same scalar–vector distinction: momentum is a vector while pressure, energy and work are scalars — the exact skill needed to know electric potential is a scalar.
- practice — not a real PYQ
Which one of the following is a scalar quantity?
- (a)Electric field
- (b)Velocity
- (c)Electric potential
- (d)Force
Answer(c) Electric potential — it has magnitude (volts) but no direction, hence scalar.
- practice — not a real PYQ
The electric field is related to the electric potential as:
- (a)the product of potential and distance
- (b)the negative gradient (rate of change) of potential
- (c)the square of the potential
- (d)independent of the potential
Answer(b) the negative gradient of potential (E = −dV/dr) — a vector derived from the scalar potential.