Topic 10.112 min read
Coulomb's Law
Coulomb's law gives the electrostatic force between two point charges. Its magnitude is directly proportional to the product of the charge magnitudes and inversely proportional to the square of their separation. The force acts along the line joining the charges: like charges repel and unlike charges attract.
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The main idea
Two electric charges push or pull each other without touching. Coulomb's law tells us the size and direction of this electrostatic force.
- F
- magnitude of electrostatic force (N)
- q1,q2
- electric charges (C)
- r
- distance between the charges (m)
- k
- Coulomb constant (N·m²·C⁻²)
Attraction or repulsion
- Two positive charges repel.
- Two negative charges repel.
- A positive and a negative charge attract.
- The force becomes four times smaller when the distance is doubled.
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Statement of Coulomb's law
Charles Coulomb experimentally studied the force between charged bodies. For two point charges, the force of attraction or repulsion is directly proportional to the product of the charge magnitudes and inversely proportional to the square of the distance between them.
- q1,q2
- the two charges (C)
- r
- separation between the charges (m)
- F
- magnitude of the mutual force (N)
- k
- constant determined by the unit system and surrounding medium (N·m²·C⁻²)
- q1,q2
- magnitudes of the charges (C)
- r
- centre-to-centre separation (m)
When to use: Use for two stationary point charges, or suitable spherically symmetric charge distributions.
Coulomb constant and permittivity
The value of k depends on the system of units and on the medium between the charges. For charges separated by vacuum in SI units:
- \varepsilon_0
- permittivity of free space (C²·N⁻¹·m⁻²)
Point-charge condition
A point charge is an ideal charge treated as if all its charge were located at one point. An electron can normally be treated as a point charge.
An isolated uniformly charged spherical conductor also behaves like a point charge for any point outside the sphere. Its external electric effect is the same as if all charge were concentrated at its centre.
Direction and vector form
Electrostatic force is a vector and must include direction. The force acts along the straight line joining the two charges.
- \vec F_{12}
- force on charge q₁ due to charge q₂ (N)
- \hat r_{12}
- unit vector specifying the force direction (none)
- \vec F_{21}
- force on charge q₂ due to charge q₁ (N)
The two charges exert forces that are equal in magnitude and opposite in direction. Coulomb's force therefore satisfies Newton's third law.
Like and unlike charges
| Signs of q₁ and q₂ | Product q₁q₂ | Force |
|---|---|---|
| Same signs | Positive | Repulsive; each charge is pushed away from the other |
| Opposite signs | Negative | Attractive; each charge is pulled toward the other |
Inverse-square dependence
| Change in separation | New force |
|---|---|
| r→2r | F→F/4 |
| r→3r | F→F/9 |
| r→r/2 | F→4F |
Effect of doubling distance
Two charges exert a force F on each other at separation r. Find the force when their separation becomes 2r.
- Initial force: F=k|q₁q₂|/r²
- New separation: 2r
F′=k|q₁q₂|/(2r)²
F′=k|q₁q₂|/(4r²)
F′=F/4
Final answer: The force becomes one-fourth of its original value.
Electrostatic and gravitational forces
Both electrostatic and gravitational forces act at a distance, so both are field forces. Each follows an inverse-square law and acts along the line joining the interacting bodies.
| Feature | Electrostatic force | Gravitational force |
|---|---|---|
| Source property | Electric charge | Mass |
| Nature | Attractive or repulsive | Always attractive |
| Distance dependence | 1r² | 1r² |
| Relative strength for elementary particles | Much stronger | Much weaker |
Exam-ready method
- Write all charges in coulombs and separation in metres.
- Use F=k|q₁q₂|/r² for magnitude.
- Draw the line joining the charges and decide attraction or repulsion from their signs.
- State the direction with the final force.
- For mutual forces, write F⃗₂₁=−F⃗₁₂.
- For more than two charges, calculate separate forces and add them as vectors using superposition.
Exam Focus
Exam Focus
Important points
- Statement and magnitude formula.
- Value and meaning of k and ε₀.
- Point-charge and isolated-sphere conditions.
- Vector direction and Newton's third-law pair.
- Like-charge repulsion and unlike-charge attraction.
Important formulas
- F=k|q1q2|r2
- k=14πε0
- F21=- F12
Common exam traps
- Square the full separation in metres.
- Use magnitude bars for F, then determine direction from charge signs.
Long question structure
Definition → proportionalities → combined formula → constants → applicability → vector direction → attraction/repulsion → Newton's third law
Common Mistakes
Common Mistakes
- Mistake
Using centimetres instead of metres or microcoulombs instead of coulombs in SI calculations.
- Mistake
Forgetting that distance is squared in Coulomb's law.
- Mistake
Using signed charge values inside a magnitude calculation without separately deciding direction.
- Mistake
Treating a nearby distorted charged sphere as an ideal point charge without checking symmetry.
- Mistake
Giving only a force magnitude when the question asks for a vector force.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Electrostatics studies charges at rest and the forces between them.
Coulomb's law applies directly to point charges and to isolated, uniformly charged spherical conductors when measured from their centres.
The force magnitude is F=k|q₁q₂|/r².
In vacuum, k=14πε₀≈9.0×10⁹ N·m²·C⁻².
Coulomb's law states that electrostatic force is directly proportional to the product of the charge magnitudes and inversely proportional to the square of their separation.
F=k|q1q2|r2=14πε0|q1q2|r2
- Definition
- Coulomb's law states that electrostatic force is directly proportional to the product of the charge magnitudes and inversely proportional to the square of their separation.
- Formula
- F=k|q1q2|r2=14πε0|q1q2|r2
- Example
- Doubling separation reduces the force to one-fourth.
- Critical warning
- Always convert charges to coulombs and distance to metres before substitution.
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Exam Practice
Important Question
Q1. State and explain Coulomb's law.
Formula
Q2. Write Coulomb's law in terms of the permittivity of free space.
Concept
Q3. When can a charged spherical conductor be treated as a point charge?
Reasoning
Q4. Show that the mutual electrostatic forces obey Newton's third law.
Comparison
Q5. Compare electrostatic force with gravitational force.