Definition
Electric potential
Work done per unit positive test charge to bring it from infinity to a point in an electric field: V = W/q. SI unit: volt (V) = J/C. Scalar quantity.
-- NCERT Class 12 Physics, Ch. 2, p. 48Electric Potential
8 MCQs1 revision card9-step worked example
Source: NCERT ElectrostaticsPYQ coverage: NEET 2020, 2021, 2022, 2024, 2026Official key: NTA-verifiedLast updated: 21 Sep 2026
Electric Potential, explained for NEET
The trap: adding potentials like vectors. Potential is a scalar. When several charges act on a point, NCERT Class 12 Physics Part I, Chapter 2 (Section 2.5, Eq. 2.17, page 51) says the total potential is the algebraic sum of the individual potentials. Signs matter; directions do not. Two equal positive charges do not "cancel" at their midpoint — their potentials add.
Definition. With potential taken as zero at infinity, the electrostatic potential at a point is the work done by an external force in bringing a unit positive charge, without acceleration, from infinity to that point (NCERT Chapter 2, Section 2.2, pages 47–48). Its unit is the volt.
Point charge. For a charge Q at distance r:
V = Q / (4πε₀ r) (NCERT Chapter 2, Eq. 2.8, page 48)
The formula holds for either sign: for Q < 0, V < 0 (page 49). V falls as 1/r, while the field of the same charge falls as 1/r² (page 49).
Dipole. For a dipole with moment p, at distance r ≫ a and angle θ from p:
V = p cos θ / (4πε₀ r²) (NCERT Chapter 2, Eq. 2.14, page 50; vector form Eq. 2.15, page 51)
On the axis V = ± p/(4πε₀r²) (Eq. 2.16, page 51: positive for θ = 0, negative for θ = π). On the equatorial plane (θ = π/2) the potential is zero. The dipole potential falls as 1/r², not 1/r, and it depends on the angle as well as on r (page 51).
System of charges. V = (1/4πε₀)(q₁/r₁P + q₂/r₂P + … + qₙ/rₙP) (Eq. 2.18, page 52). Each rᵢP is the distance from that charge to P.
Bridge to NEET. The usual pattern asks for the total potential at a point due to a set of charges. Distractors come from vector-style cancellation, dropping a sign, using r² instead of r, or using the wrong distance.
Watch out: a zero potential does not mean a zero field, and a zero field does not mean a zero potential. Compute each separately.
Can you answer these Electric Potential MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
Taking the potential at infinity to be zero, the electrostatic potential at a point P is:
Show answer and why every option is right or wrong
Answer: B. NCERT Class 12 Physics Part I, Chapter 2, Section 2.2 (pages 47–48) defines the potential at a point as the work done by an external force in bringing a unit positive charge, without acceleration, from infinity to that point.
Why A is wrong: A is wrong because the force on a unit positive charge is the electric field at P, a vector; potential is work per unit charge, a scalar.
Why C is wrong: C is wrong because it reverses the path: taking the charge from P to infinity needs work equal to minus the potential at P, not the potential itself.
Why D is wrong: D is wrong because the work to bring a charge q is proportional to q; NCERT divides the work by the charge so that potential does not depend on the test charge.
MCQ 2Easy RecallPractice
At large distances r from an electric dipole, its electrostatic potential varies as:
Show answer and why every option is right or wrong
Answer: D. NCERT Class 12 Physics Part I, Chapter 2 (Eq. 2.15 and point (ii), page 51): the dipole potential falls off at large distance as 1/r², not as 1/r.
Why A is wrong: A is wrong because 1/r is the fall-off of the potential of a single point charge, not of a dipole.
Why B is wrong: B is wrong because the dipole potential p cos θ/(4πε₀r²) clearly changes with r.
Why C is wrong: C is wrong because 1/r³ is how the electric field of a dipole falls off at large distance (NCERT page 50), not its potential.
MCQ 3Easy RecallPractice
For a short electric dipole of moment p, what is the electrostatic potential at a point at distance r on its equatorial plane (θ = π/2)?
Show answer and why every option is right or wrong
Answer: A. With θ = π/2, cos θ = 0, so V = p cos θ/(4πε₀r²) = 0. NCERT Class 12 Physics Part I, Chapter 2, page 51 states that the potential in the equatorial plane is zero.
Why B is wrong: B is wrong because −p/(4πε₀r²) is the potential on the axis at θ = π, where cos θ = −1.
Why C is wrong: C is wrong because p/(4πε₀r²) is the potential on the axis at θ = 0, where cos θ = 1.
Why D is wrong: D is wrong because p/(4πε₀r³) is the magnitude of the equatorial electric field, not the potential; the field there is not zero even though the potential is.
MCQ 4Direct ApplicationPractice
What is the electrostatic potential at a point 15 cm from a point charge of −3.0 × 10⁻⁹ C? (Take 1/4πε₀ = 9 × 10⁹ N m² C⁻² and V = 0 at infinity.)
Show answer and why every option is right or wrong
Answer: D. V = (9 × 10⁹)(−3.0 × 10⁻⁹)/0.15 = −27/0.15 = −1.8 × 10² V. For a negative charge the potential is negative (NCERT Class 12 Physics Part I, Chapter 2, Eq. 2.8, pages 48–49).
Why A is wrong: A is wrong because it uses the magnitude 27/0.15 = 180 V and drops the negative sign of the charge; for Q < 0, V < 0.
Why B is wrong: B is wrong because −1.8 V comes from dividing by 15 (the distance in centimetres) instead of 0.15 m.
Why C is wrong: C is wrong because −1.2 × 10³ V comes from dividing by r² = 0.0225 m² (−27/0.0225 = −1200 V); potential goes as 1/r, not 1/r².
MCQ 5Direct ApplicationPractice
Two point charges, each +4.0 × 10⁻⁹ C, are placed 0.20 m apart. What is the electrostatic potential at the midpoint of the line joining them? (Take 1/4πε₀ = 9 × 10⁹ N m² C⁻².)
Show answer and why every option is right or wrong
Answer: C. Each charge is 0.10 m from the midpoint and gives (9 × 10⁹)(4.0 × 10⁻⁹)/0.10 = 3.6 × 10² V. Potentials add algebraically: V = 2 × 3.6 × 10² = 7.2 × 10² V (NCERT Class 12 Physics Part I, Chapter 2, Eq. 2.17, page 51).
Why A is wrong: A is wrong because it treats the two potentials like opposite vectors that cancel; potential is a scalar, and two positive potentials add.
Why B is wrong: B is wrong because 3.6 × 10² V is the potential due to only one of the two charges.
Why D is wrong: D is wrong because 7.2 × 10³ V comes from dividing by r² = 0.010 m² for each charge (2 × 36/0.010 = 7200 V); potential goes as 1/r.
MCQ 6Direct ApplicationPractice
A short electric dipole has dipole moment 2.0 × 10⁻¹¹ C m. What is the potential at a point on its axis, 0.30 m from its centre, on the side of the positive charge (θ = 0)? (Take 1/4πε₀ = 9 × 10⁹ N m² C⁻².)
Show answer and why every option is right or wrong
Answer: C. On the axis at θ = 0, V = p/(4πε₀r²) = (9 × 10⁹)(2.0 × 10⁻¹¹)/(0.30)² = 0.18/0.090 = 2.0 V (NCERT Class 12 Physics Part I, Chapter 2, Eq. 2.16, page 51).
Why A is wrong: A is wrong because 0.60 V comes from dividing by r = 0.30 m (0.18/0.30), using the point-charge 1/r dependence instead of the dipole's 1/r².
Why B is wrong: B is wrong because 6.7 V comes from dividing by r³ = 0.027 m³ (0.18/0.027), the distance dependence of the dipole field, not its potential.
Why D is wrong: D is wrong because zero is the potential on the equatorial plane (θ = π/2); on the axis cos θ = 1.
MCQ 7CalculationPractice
A charge +6.0 × 10⁻⁹ C is at x = 0 and a charge −2.0 × 10⁻⁹ C is at x = 0.40 m. Taking V = 0 at infinity, at what point between the two charges is the electrostatic potential zero?
Show answer and why every option is right or wrong
Answer: B. Set 6.0/x − 2.0/(0.40 − x) = 0, so 6.0(0.40 − x) = 2.0x, giving 2.4 = 8.0x and x = 0.30 m. Check: 6.0/0.30 = 20 and 2.0/0.10 = 20, so the two potentials cancel algebraically (NCERT Class 12 Physics Part I, Chapter 2, Eq. 2.18, page 52).
Why A is wrong: A is wrong because 0.10 m is the distance of the zero-potential point from the −2.0 × 10⁻⁹ C charge, not its x-coordinate measured from the origin.
Why C is wrong: C is wrong because the midpoint would give zero only for charges of equal magnitude; here 6.0/0.20 − 2.0/0.20 = 20, not zero.
Why D is wrong: D is wrong because x = 0.60 m also gives zero potential (6.0/0.60 = 2.0/0.20), but it lies beyond the negative charge, not between the two charges.
MCQ 8CalculationPractice
Four point charges, +2.0 × 10⁻⁹ C, +3.0 × 10⁻⁹ C, −4.0 × 10⁻⁹ C and +1.0 × 10⁻⁹ C, sit at the corners of a square, each 0.10 m from the centre. What is the electrostatic potential at the centre? (Take 1/4πε₀ = 9 × 10⁹ N m² C⁻².)
Show answer and why every option is right or wrong
Answer: A. All four charges are at the same distance, so V = (9 × 10⁹)(Σq)/0.10. Σq = (2.0 + 3.0 − 4.0 + 1.0) × 10⁻⁹ = 2.0 × 10⁻⁹ C, so V = 18/0.10 = 1.8 × 10² V (NCERT Class 12 Physics Part I, Chapter 2, Eq. 2.18, page 52).
Why B is wrong: B is wrong because 9.0 × 10² V comes from adding the magnitudes (2.0 + 3.0 + 4.0 + 1.0 = 10 × 10⁻⁹ C) and ignoring the negative sign of one charge.
Why C is wrong: C is wrong because 1.8 × 10³ V comes from dividing by r² = 0.010 m² (18/0.010); potential goes as 1/r.
Why D is wrong: D is wrong because 5.4 × 10² V comes from leaving out the −4.0 × 10⁻⁹ C charge (Σq = 6.0 × 10⁻⁹ C, 54/0.10 = 540 V).
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Electric Potential: quick recall before you leave
How do you solve a Electric Potential question? A worked example
- 1
Given
A point charge of 4 × 10⁻⁷ C. Point P is 9 cm (= 0.09 m) from it. A second charge of 2 × 10⁻⁹ C is to be brought from infinity to P. Take 1/4πε₀ = 9 × 10⁹ N m² C⁻² and V = 0 at infinity. (NCERT Class 12 Physics Part I, Chapter 2, Example 2.1, page 49.)
- 2
Required
(a) The potential at P. (b) The work done in bringing the 2 × 10⁻⁹ C charge from infinity to P, and whether this work depends on the path.
- 3
Concept
The potential at P is the work per unit positive charge to bring a charge from infinity to P. For a point charge it is V = Q/(4πε₀r). The work to bring a charge q from infinity is then q times that potential.
- 4
Formula
V = (1/4πε₀) Q/r ; W = qV
- 5
Substitution
(a) V = (9 × 10⁹ N m² C⁻²) × (4 × 10⁻⁷ C) / (0.09 m)
(b) W = (2 × 10⁻⁹ C) × V - 6
Calculation
(a) Numerator: 9 × 10⁹ × 4 × 10⁻⁷ = 36 × 10² = 3.6 × 10³. Then 3.6 × 10³ / 0.09 = 4 × 10⁴ V.
(b) W = 2 × 10⁻⁹ × 4 × 10⁴ = 8 × 10⁻⁵ J.
The factor 100 used to convert 9 cm to 0.09 m is exact and does not affect significant figures. The data are given to one significant figure, and 9 × 10⁹ is the rounded value of 1/4πε₀, so the answers are reported to one significant figure, as NCERT does. - 7
Final answer
(a) V = 4 × 10⁴ V; (b) W = 8 × 10⁻⁵ J. No, the work does not depend on the path. NCERT's reason: any small displacement can be split into a part along r and a part perpendicular to r, and the perpendicular part does no work.
- 8
Common trap
Dividing by r² gives 3.6 × 10³/0.0081 ≈ 4.4 × 10⁵, which is the magnitude of the field in N/C, not the potential in volts. Leaving r as 9 (in cm) gives 4 × 10² V, a factor of 100 too small.
- 9
Similar NEET-style question
"Find the electrostatic potential at a point 12 cm from a point charge of −6.0 × 10⁻⁹ C. (Take 1/4πε₀ = 9 × 10⁹ N m² C⁻².)"
Strategy: V = (9 × 10⁹)(−6.0 × 10⁻⁹)/0.12 = −54/0.12 = −4.5 × 10² V. Keep the negative sign, use r in metres, and divide by r, not r².
---
What to remember before solving Electric Potential questions
V = (1/4πε₀)(q/r). Falls off as 1/r. V → 0 as r → ∞ (chosen reference).
-- NCERT Class 12 Physics, Ch. 2, p. 48Formula
Potential due to dipole
V = (1/4πε₀)(p cos θ)/r², where θ is angle from dipole axis. Falls off as 1/r² (faster than point charge). V = 0 on equatorial plane.
-- NCERT Class 12 Physics, Ch. 2, p. 51V_total = Σ V_i (algebraic sum since V is scalar). For continuous: V = (1/4πε₀) ∫ dq/r.
-- NCERT Class 12 Physics, Ch. 2, p. 52Formula
Relation between E and V
E = -dV/dr (1D); E = -∇V (3D). Field points from high to low potential. |E| = |dV/dr| in the direction of steepest decrease.
-- NCERT Class 12 Physics, Ch. 2, p. 55Which Electric Potential formulas do you need for NEET?
1 formula — click to collapse
Electric potential of point charge
Scalar potential at distance r from point charge q, with V→0 at infinity.
| Symbol | Quantity | SI Unit |
|---|---|---|
| V | potential | V |
| q | point charge | C |
| r | distance | m |
Valid when
- Reference V=0 at infinity
More in Electrostatics: 3 exam traps and mistakes · 10 formulas · 5 question patterns from its other lessons.
Electric Potential questions from past NEET papers
5 questions from NEET 2020, 2021, 2022, 2024, 2026. Answers verified against NTA official keys. — click to collapse
NEET 2026
1√(3Qq/(4πε₀mR))
2√(2Qq/(3πε₀mR))
3√(Qq/(3πε₀mR))
4√(Qq/(4πε₀mR))
NTA Answer: Option 3(final)
NEET 2024Revised key
1Both A and R are true and R is the correct explanation of A.
2Both A and R are true and R is NOT the correct explanation of A.
3A is true but R is false.
4A is false but R is true.
NTA Answer: Option 3(revised_final)
NEET 2022
1Dependent on the material property of the sphere
2More on bigger sphere
3More on smaller sphere
4Equal on both the spheres
NTA Answer: Option 3(final)
NEET 2021
11980 V
2660 V
31320 V
41520 V
NTA Answer: Option 1(final)
NEET 2020
15 N/C
2zero
30.5 N/C
41 N/C
NTA Answer: Option 2(final)
How does NEET ask about Electric Potential?
1 recurring pattern from past papers — click to collapse
Total potential at a point = scalar sum of potentials from each charge.
Multi StepMedium
Common distractors
uses vector sum
Adds V as vector instead of scalar
Sources
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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