PhysicsChapter 10: Electrostatics
Coulomb's Law
Explanation level
Electrostatics and electric charge
Matter is made of atoms containing protons, neutrons and electrons. A proton carries positive charge, an electron carries an equal amount of negative charge, and a neutron has no net charge.
A neutral atom contains equal numbers of protons and electrons. Removing an electron leaves a net positive charge, while adding an electron gives a net negative charge. Electrostatics is the study of charges at rest and the forces between them.
Charged comb
Situation: A comb is rubbed through dry hair and then brought near small paper pieces.
Explanation: The rubbing transfers charge to the comb. The charged comb attracts the paper pieces through electrostatic induction.
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.
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Exam preparation
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.
Common mistakes
- Using centimetres instead of metres or microcoulombs instead of coulombs in SI calculations.
- Forgetting that distance is squared in Coulomb's law.
- Using signed charge values inside a magnitude calculation without separately deciding direction.
- Treating a nearby distorted charged sphere as an ideal point charge without checking symmetry.
- Giving only a force magnitude when the question asks for a vector force.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Coulomb's Law
Sticky Notes — Quick Revision
Key Point 1
- The force magnitude is F=k|q₁q₂|/r².
Key Point 2
- In vacuum, k=14πε₀≈9.0×10⁹ N·m²·C⁻².
Key Point 3
- Like charges repel, whereas unlike charges attract.
Key Point 4
- The mutual forces obey Newton's third law: F⃗₂₁=−F⃗₁₂.
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- 8 concept questions
- Easy → Medium → Hard
- Explanation after each answer
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.
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