Force between two point charges q₁ and q₂ separated by distance r in vacuum: F = (1/4πε₀) q₁q₂/r², directed along the line joining them. 1/(4πε₀) ≈ 9 × 10⁹ N·m²/C².
-- NCERT Class 12 Physics, Ch. 1, p. 7Coulomb's Law
8 MCQs1 revision card9-step worked example
Source: NCERT ElectrostaticsOfficial key: NTA-verifiedLast updated: 21 Sep 2026
Coulomb's Law, explained for NEET
The trap: writing F = q₁q₂/r² and stopping there. The constant is not optional. Drop it and a force of about 0.6 N turns into something like 10⁻¹¹ N. A second common slip is dividing by r instead of r², and a third is leaving microcoulombs unconverted.
The law. NCERT Class 12 Physics Part I, Chapter 1 (Section 1.5, page 6) states that the force between two point charges varies inversely as the square of the distance between them, is directly proportional to the product of their magnitudes, and acts along the line joining them. In vacuum:
F = k q₁q₂ / r² (NCERT Chapter 1, Eq. 1.1, page 7)
In SI units k is about 9 × 10⁹ N m² C⁻² (page 7). NCERT writes k = 1/4πε₀ (Eq. 1.2, page 8), where ε₀ = 8.854 × 10⁻¹² C² N⁻¹ m⁻² is the permittivity of free space. Do not confuse the two numbers: k is large, ε₀ is tiny.
What the law also says.
- Point charges: the sizes of the charged bodies must be much smaller than their separation (page 6).
- Direction (Eq. 1.3, page 8): like charges repel, unlike charges attract; one vector equation covers both signs.
- The force on q₁ due to q₂ is equal and opposite to the force on q₂ due to q₁, so Coulomb's law agrees with Newton's third law (page 9). The bigger charge does not feel a bigger force.
- The law as written is for charges in vacuum; matter in between complicates things (page 9).
Bridge to NEET. The basic pattern gives q₁, q₂ and r and asks for F, or gives F and asks for r or q. Scaling questions change a charge or the distance: doubling r cuts F to one quarter.
Watch out: convert μC to C (× 10⁻⁶) and cm to m before substituting, and square r only after converting it.
Can you answer these Coulomb's Law 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
According to Coulomb's law as stated in NCERT, the electrostatic force between two point charges:
Show answer and why every option is right or wrong
Answer: B. NCERT Class 12 Physics Part I, Chapter 1, Section 1.5 (page 6): the force varies inversely as the square of the distance, is directly proportional to the product of the magnitudes of the charges, and acts along the line joining them.
Why A is wrong: A is wrong because Coulomb's law is an inverse-square law; the force goes as 1/r², not 1/r.
Why C is wrong: C is wrong because the force depends on the product q₁q₂, not on the sum of the charges.
Why D is wrong: D is wrong because the force acts along the line joining the two charges, not perpendicular to it.
MCQ 2Easy RecallPractice
In SI units, the approximate value of the constant k = 1/4πε₀ in Coulomb's law is:
Show answer and why every option is right or wrong
Answer: D. NCERT Class 12 Physics Part I, Chapter 1 (page 7) gives k ≈ 9 × 10⁹ N m² C⁻², and page 8 writes it as 1/4πε₀.
Why A is wrong: A is wrong because 6.67 × 10⁻¹¹ is the numerical value of the gravitational constant G, not the Coulomb constant.
Why B is wrong: B is wrong because 8.854 × 10⁻¹² is the value of ε₀ itself, whose unit is C² N⁻¹ m⁻²; k is 1/4πε₀, not ε₀.
Why C is wrong: C is wrong because the exponent has the wrong sign; k is a very large number, 9 × 10⁹.
MCQ 3Easy RecallPractice
Two point charges +q and +4q are held some distance apart in vacuum. The force on +q due to +4q has magnitude F. The force on +4q due to +q is:
Show answer and why every option is right or wrong
Answer: A. NCERT Class 12 Physics Part I, Chapter 1 (page 9): F₁₂ = −F₂₁, so Coulomb's law agrees with Newton's third law. Both charges feel forces of equal magnitude in opposite directions.
Why B is wrong: B is wrong because the magnitude depends on the product q × 4q, which is the same for both charges, so neither force is divided by 4.
Why C is wrong: C is wrong because the larger charge does not feel a larger force; the product q₁q₂ is shared by both, so both magnitudes equal F.
Why D is wrong: D is wrong because it scales the force by the larger charge and keeps the same direction; the two forces are equal in magnitude and opposite in direction.
MCQ 4Direct ApplicationPYQ Pattern
Two point charges of 2.0 μC and 3.0 μC are 0.30 m apart in vacuum. Taking k = 9.0 × 10⁹ N m² C⁻², the magnitude of the force between them is:
Show answer and why every option is right or wrong
Answer: C. F = kq₁q₂/r² = 9.0 × 10⁹ × (2.0 × 10⁻⁶)(3.0 × 10⁻⁶) / (0.30)² = 5.4 × 10⁻² / 0.090 = 0.60 N (NCERT Chapter 1, Eq. 1.1, page 7).
Why A is wrong: A is wrong because 6.7 × 10⁻¹¹ N comes from q₁q₂/r² = 6.0 × 10⁻¹² / 0.090 with the constant k left out.
Why B is wrong: B is wrong because 0.18 N comes from dividing by r = 0.30 m instead of r² = 0.090 m²: 5.4 × 10⁻² / 0.30 = 0.18.
Why D is wrong: D is wrong because 6.0 × 10¹¹ N comes from substituting 2.0 and 3.0 as coulombs instead of converting microcoulombs: 9.0 × 10⁹ × 6.0 / 0.090.
MCQ 5Direct ApplicationPYQ Pattern
Two point charges in vacuum repel each other with a force of 8.0 N. If the distance between them is doubled with the charges unchanged, the force becomes:
Show answer and why every option is right or wrong
Answer: C. F ∝ 1/r², so doubling r divides F by 2² = 4: 8.0 N / 4 = 2.0 N (NCERT Chapter 1, Eq. 1.1, page 7).
Why A is wrong: A is wrong because 4.0 N = 8.0/2 treats the force as varying with 1/r instead of 1/r².
Why B is wrong: B is wrong because 16 N = 8.0 × 2 treats the force as increasing in proportion to r.
Why D is wrong: D is wrong because 32 N = 8.0 × 4 applies the factor r² in the numerator instead of the denominator.
MCQ 6Direct ApplicationPYQ Pattern
Point charges of 1.0 μC and 4.0 μC are placed in vacuum. Taking k = 9.0 × 10⁹ N m² C⁻², at what separation is the force between them 0.90 N?
Show answer and why every option is right or wrong
Answer: A. r² = kq₁q₂/F = 9.0 × 10⁹ × (1.0 × 10⁻⁶)(4.0 × 10⁻⁶) / 0.90 = 3.6 × 10⁻² / 0.90 = 0.040 m², so r = 0.20 m (NCERT Chapter 1, Eq. 1.1, page 7).
Why B is wrong: B is wrong because 2.1 × 10⁻⁶ m comes from r² = q₁q₂/F = 4.0 × 10⁻¹² / 0.90 with k left out, giving r ≈ 2.1 × 10⁻⁶ m.
Why C is wrong: C is wrong because 2.0 × 10⁵ m comes from using 1.0 and 4.0 as coulombs: r² = 9.0 × 10⁹ × 4.0 / 0.90 = 4.0 × 10¹⁰ m².
Why D is wrong: D is wrong because 0.040 is r², not r; the square root was not taken.
MCQ 7CalculationPractice
Two point charges in vacuum exert a force F on each other when they are a distance r apart. One charge is tripled and the separation is increased to 3r. The new force is:
Show answer and why every option is right or wrong
Answer: B. The product q₁q₂ becomes 3 times larger and r² becomes 9 times larger, so F′ = F × 3/9 = F/3 (NCERT Chapter 1, Eq. 1.1, page 7).
Why A is wrong: A is wrong because F = F × 3/3 uses a 1/r dependence; the distance factor must be squared, giving 9 in the denominator.
Why C is wrong: C is wrong because F/9 applies only the distance change and forgets that one charge was tripled.
Why D is wrong: D is wrong because 3F applies only the charge change and forgets that the separation was tripled.
MCQ 8CalculationPractice
A point charge q₁ = +3.0 μC is at the origin and a point charge q₂ = −5.0 μC is at x = +0.50 m, in vacuum. Taking k = 9.0 × 10⁹ N m² C⁻², the force on q₂ is:
Show answer and why every option is right or wrong
Answer: D. Magnitude: F = 9.0 × 10⁹ × (3.0 × 10⁻⁶)(5.0 × 10⁻⁶) / (0.50)² = 0.135 / 0.25 = 0.54 N. The charges have opposite signs, so the force is attractive: q₂ is pulled toward q₁ at the origin, along −x (NCERT Chapter 1, Eq. 1.3, page 8).
Why A is wrong: A is wrong because it has the right magnitude but treats the pair as repelling; unlike charges attract, so q₂ is pulled toward the origin, along −x.
Why B is wrong: B is wrong because 0.27 N comes from dividing by r = 0.50 m instead of r² = 0.25 m²: 0.135 / 0.50 = 0.27.
Why C is wrong: C is wrong because 0.14 N is kq₁q₂ = 0.135 rounded, with the division by r² left out.
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Coulomb's Law: quick recall before you leave
How do you solve a Coulomb's Law question? A worked example
- 1
Given
NCERT Class 12 Physics Part I, Chapter 1, Example 1.3 (pages 9–10). An electron and a proton are 1 Å (= 10⁻¹⁰ m) apart. Charge magnitude e = 1.6 × 10⁻¹⁹ C; k = 8.987 × 10⁹ N m²/C² (the value used in NCERT's solution); m_p = 1.67 × 10⁻²⁷ kg; m_e = 9.11 × 10⁻³¹ kg.
- 2
Required
(a) How strong the electric force is compared with the gravitational force, as the ratio of their magnitudes, for an electron and a proton and for two protons. (b) The magnitude of the electric force between the electron and the proton at 1 Å, and the accelerations of the electron and of the proton due to it.
- 3
Concept
Both forces follow an inverse-square law, so r cancels in the ratio F_e/F_G. The electric force on the electron and on the proton has the same magnitude (Newton's third law), but the masses differ, so the accelerations differ (a = F/m).
- 4
Formula
|F_e| = (1/4πε₀) e²/r²; F_e/F_G = e² / (4πε₀ G m_p m_e); a = F/m.
- 5
Substitution
(b) |F| = 8.987 × 10⁹ × (1.6 × 10⁻¹⁹)² / (10⁻¹⁰)²
a_electron = |F| / 9.11 × 10⁻³¹ kg
a_proton = |F| / 1.67 × 10⁻²⁷ kg - 6
Calculation
(a) NCERT reports F_e/F_G ≈ 2.4 × 10³⁹ for an electron and a proton, and ≈ 1.3 × 10³⁶ for two protons. The distance r cancels, so the ratio is the same at every separation.
(b) (1.6 × 10⁻¹⁹)² = 2.56 × 10⁻³⁸; divided by (10⁻¹⁰)² = 10⁻²⁰ gives 2.56 × 10⁻¹⁸; times 8.987 × 10⁹ gives |F| = 2.3 × 10⁻⁸ N.
a_electron = 2.3 × 10⁻⁸ / 9.11 × 10⁻³¹ = 2.5 × 10²² m/s²
a_proton = 2.3 × 10⁻⁸ / 1.67 × 10⁻²⁷ = 1.4 × 10¹⁹ m/s²
The separation 1 Å = 10⁻¹⁰ m is an exact unit conversion, and the squaring exponent 2 is an exact counting number; neither limits the significant figures. The answers follow NCERT's two significant figures. - 7
Final answer
(a) F_e/F_G ≈ 2.4 × 10³⁹ (electron–proton) and ≈ 1.3 × 10³⁶ (proton–proton). (b) |F| = 2.3 × 10⁻⁸ N; electron acceleration 2.5 × 10²² m/s²; proton acceleration 1.4 × 10¹⁹ m/s².
- 8
Common trap
Giving the proton the same acceleration as the electron, or giving the proton a larger force because it is heavier. The forces are equal in magnitude; the proton's acceleration is smaller because its mass is about 1800 times larger. Also, the ratio in (a) does not depend on r, so no distance is needed there.
- 9
Similar NEET-style question
"Two point charges of +5.0 nC each are 3.0 cm apart in vacuum. Taking k = 9.0 × 10⁹ N m² C⁻², find the force between them and say whether it is attractive or repulsive."
Strategy: Convert first: 5.0 nC = 5.0 × 10⁻⁹ C, 3.0 cm = 3.0 × 10⁻² m. F = 9.0 × 10⁹ × (5.0 × 10⁻⁹)² / (3.0 × 10⁻²)² = 2.25 × 10⁻⁷ / 9.0 × 10⁻⁴ = 2.5 × 10⁻⁴ N, repulsive (like charges). Dividing by r instead of r² would give 7.5 × 10⁻⁶ N.
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What to remember before solving Coulomb's Law questions
Which Coulomb's Law formulas do you need for NEET?
1 formula — click to collapse
Coulomb's law
Force between two point charges in vacuum. 1/(4*pi*eps0) ~ 9e9 N*m^2/C^2.
| Symbol | Quantity | SI Unit |
|---|---|---|
| F | force | N |
| q1,q2 | charges | C |
| r | separation | m |
| eps0 | permittivity 8.85e-12 | F/m |
Valid when
- Point charges (or spherically symmetric)
- r > body sizes
More in Electrostatics: 3 exam traps and mistakes · 10 formulas · 5 question patterns from its other lessons.
Coulomb's Law questions from past NEET papers
No question in our NEET 2020–2025 set targets this topic directly.
How does NEET ask about Coulomb's Law?
1 recurring pattern from past papers — click to collapse
Force between two point charges; given q1, q2, r, find F.
Direct ApplicationEasy
Common distractors
forgets 1 over 4pi eps0
Uses naive q1q2/r^2 without constant
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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