#electric force

Coulomb's Law and Force Between Point Charges

Two point charges \( 9 \times 10^{-7} \, \text{C} \) and \( -3 \times 10^{-7} \, \text{C} \) are 100 cm apart in vacuum.

**Coulomb's law** gives force between point charges as F = k·|q₁q₂|/r², k = 1/(4π ε₀) = 9×10⁹ N·m²/C², directed along line joining charges. Like charges repel, opposite attract, magnitude scales with product of charges and inverse square of separation r². Using Coulomb’s law: F = k (|q₁ q₂|/r²) . k = 9 × 10⁹ N·m²/C² , q₁ = 9 × 10⁻⁷ C , q₂ = -3 × 10⁻⁷ C , r = 1.0 m . |q₁ q₂| = 9 × 3 × 10⁻¹⁴ = 27 × 10⁻¹⁴ C² . r² = (1.0)² = 1 m² . F = 9 × 10⁹ × (27 × 10⁻¹⁴/1)

Ref: NCERT > Physics Book > Electric Charges and Fields > Coulomb's Law and Force Between Point Charges

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Electric Charge, Quantization and Conservation

Two charges \( +3 \, \mu\text{C} \) and \( -3 \, \mu\text{C} \) are 15 cm apart. What is the force on a \( 2 \, \mu\text

**Charge conservation and quantization** govern rubbing processes where electrons transfer without creation. Total charge before and after remains equal, and any measured charge corresponds to n = q/e electrons, allowing counting of carriers from coulomb value. Electric field at midpoint: E₁ = 9 × 10⁹ × (3 × 10⁻⁶/(0.075)²) = 4.8 × 10⁶ N/C (towards -3 μC ). E₂ = 4.8 × 10⁶ N/C (towards -3 μC ). Net E = 4.8 × 10⁶ + 4.8 × 10⁶ = 9.6 × 10⁶ N/C . Force: F = q E = 2 × 10⁻⁶ × 9.6 × 10⁶ = 19.2 N . Substituting values gives 19.2

Ref: NCERT > Physics Book > Electric Charges and Fields > Electric Charge, Quantization and Conservation

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Coulomb's Law and Force Between Point Charges

Three charges \( +q, +q, -q \) are at the vertices of an equilateral triangle of side 3 m. What is the net force magnitu

**Electrostatic force** described by F = (1/4π ε₀)·q₁q₂/r² obeys Newton's third law. Magnitude depends on q₁q₂ and 1/r², enabling quantitative estimation at given separation, with sign indicating attraction or repulsion. Force between +q and +q : F = (k q²/(3)²) = (k q²/9) (repulsive). Force between +q and -q : F = (k q²/9) (attractive). Angle between forces is 60°. Resultant: Fₙₑt = √(F² + F² + 2F² cos 60°) = √(3) F = (√(3) k q²/9) . Substituting values gives (√(3) k q²/9), which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

Ref: NCERT > Physics Book > Electric Charges and Fields > Coulomb's Law and Force Between Point Charges

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Superposition Principle and Equilibrium of Charges

Three charges \( +8 \, \mu\text{C}, -4 \, \mu\text{C}, +2 \, \mu\text{C} \) are at the vertices of an equilateral triang

**Vector addition of forces** underlies multi-charge analysis. Each pair contributes independent Coulomb force, resultant obtained by resolving components along axes. Equilibrium occurs when vector sum vanishes, often at symmetric points where contributions balance. F₁ = 9 × 10⁹ × (8 × 4 × 10⁻¹²/(1.8)²) = 0.0889 N (attractive). F₂ = 9 × 10⁹ × (8 × 2 × 10⁻¹²/(1.8)²) = 0.0444 N (repulsive). Angle 60°. Net F = √(F₁² + F₂² + 2 F₁ F₂ cos 60°) = √(0.0889² + 0.0444² + 0.00395) = 0.108 N . Substituting values gives 0.108 N, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

Ref: NCERT > Physics Book > Electric Charges and Fields > Superposition Principle and Equilibrium of Charges

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