Coulomb's Law

• Coulomb's law for force between point charges in vacuum and medium.
• The superposition principle for multiple charges — vector addition of forces.
• Comparison with Newton's gravitation: similar inverse-square form, different nature (attractive/repulsive).
• To apply free-body diagrams and resolve components in 2D charge arrangements.
• Permittivity ε₀, relative permittivity K, and force in dielectric: F = (1/4πε₀K)(q₁q₂/r²).

Level 1 — Foundations

Verbal: Coulomb's law states that two point charges exert equal and opposite forces along the line joining them, proportional to product of charges and inversely proportional to square of distance.

Scalar magnitude: F = (1/4πε₀) |q₁q₂|/r² in vacuum.

Vector form: F⃗₁₂ = (1/4πε₀)(q₁q₂/r²) r̂₁₂ where r̂₁₂ points from q₁ to q₂.

Nature: Like charges repel; unlike charges attract.

Constants: k = 1/4πε₀ ≈ 9 × 10⁹ N·m²/C²; ε₀ ≈ 8.854 × 10⁻¹² C²/N·m².

Point charge assumption: Valid when charge dimensions ≪ separation distance.

Level 2 — JEE / NEET depth

In medium: Force reduced by factor K (dielectric constant): F_medium = F_vacuum/K.

Superposition: Net force on a charge = vector sum of forces due to each other charge individually: F⃗_net = Σ F⃗ᵢ.

Comparison with gravity:

Units: SI unit of charge = coulomb (C). 1 C is large; typical problems use μC, nC.

Equilibrium of charges: Place test charge where net force zero — solve for position using vector balance (JEE favourite geometry setups: line, triangle, square vertices).

Force between two point charges

q₁ = +2 μC, q₂ = −3 μC, r = 0.3 m in air.

Step 1 — Convert: q₁ = 2×10⁻⁶ C, q₂ = −3×10⁻⁶ C.
Step 2 — F = k|q₁q₂|/r² = (9×10⁹)(6×10⁻¹²)/(0.09).
Step 3 — F = 54×10⁻³/0.09 = 0.6 N.
Step 4 — Attractive (unlike signs); magnitude on each charge is 0.6 N.

Superposition — charge at origin

+Q at origin. Find force on +q at (a, 0) due to +Q and −Q at (0, a).

Step 1 — F₁ from +Q at origin: repulsive, along +x: F₁ = kQq/a² î.
Step 2 — F₂ from −Q at (0,a): attractive toward (0,a); components need resolution.
Step 3 — Vector add F₁ + F₂; magnitude depends on geometry — always draw diagram first.
Step 4 — Symmetry may cancel components in symmetric configurations.

• State Coulomb's law in vector form.
• Compare electrostatic and gravitational force between proton and electron.
• How does force change if distance is doubled?
• Two equal charges repel with force F. Distance halved — new force?
• Stretch: Derive equilibrium position for third charge on line between two fixed charges.

NCERT Chapter 1 link: Coulomb's law is the starting point of electrostatics — superposition principle follows immediately. Use SI units consistently; charge in coulombs, distance in metres.

Exam connections: JEE combines Coulomb with mechanics — charged pendants in equilibrium as pendulum. Compare magnitude of electrostatic vs gravitational force between electron and proton — electrostatic dominates by ~10³⁹ factor at atomic scale. Vector resolution in square/hexagonal charge arrangements is recurring pattern.

Study strategy: Draw force vectors on every charge before adding. Use symmetry to cancel components. In dielectric medium, remember force divides by K — parallel with field reduction in matter chapter preview.

When studying Coulomb's Law within Electrostatics, start by listing every formula and definition on one page without looking at the textbook. Compare your list to NCERT — missing items indicate gaps to fix immediately. Work through at least two NCERT Examples for this section with steps written in full; examiners award method marks even when arithmetic slips.

For board exams (CBSE), long answers benefit from a clear structure: definition → explanation → diagram or formula → example → brief conclusion. Underline key terms. For JEE Main and NEET, prioritise conceptual traps and quick calculation paths; timed mixed quizzes of 10 questions after revision simulate exam pressure.

Cross-topic link: Calculus-based derivations assume differentiation comfort; units and dimensional analysis prevent numerical errors.

Spaced revision: Review this note at 1 day, 3 days, and 7 days after first study. Attempt the Quick check questions closed-book, then open the Practice tab for graded reinforcement. Maintain an error log — repeated mistake patterns reveal whether the issue is concept, formula recall, or careless reading.

Diagram and terminology drill: For Physics, redraw key figures from memory and define every labelled part in one sentence. Vocabulary precision prevents mark loss in descriptive answers — use NCERT terms exactly as printed in the textbook.

Revision tip: Link this topic to adjacent Class 12 chapters before attempting mixed practice.

Open the Practice tab for graded questions on Coulomb's Law.