#electrostatic force

Superposition Principle and Equilibrium of Charges

Three charges \( +5 \, \mu\text{C}, -3 \, \mu\text{C}, +4 \, \mu\text{C} \) are at the vertices of an equilateral triang

**Independent action of charges** allows total force or field as vector sum. Geometry dictates distances to evaluation point, and resultant follows Σ k q_i/r_i², explaining zero field at symmetric centres for equal charges. F₁ = 9 × 10⁹ × (5 × 3 × 10⁻¹²/(1.5)²) = 0.06 N (attractive). F₂ = 9 × 10⁹ × (5 × 4 × 10⁻¹²/(1.5)²) = 0.08 N (repulsive). Angle 60°. Net F = √(F₁² + F₂² + 2 F₁ F₂ cos 60°) = √(0.06² + 0.08² + 0.0048) = 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.

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Superposition Principle and Equilibrium of Charges

Three charges \( +5 \, \mu\text{C}, -5 \, \mu\text{C}, +2 \, \mu\text{C} \) 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 × (5 × 5 × 10⁻¹²/(1.5)²) = 0.1 N (attractive). F₂ = 9 × 10⁹ × (5 × 2 × 10⁻¹²/(1.5)²) = 0.04 N (repulsive). Angle 60°. Net F = √(F₁² + F₂² + 2 F₁ F₂ cos 60°) = √(0.1² + 0.04² + 0.004) = 0.129 N . Substituting values gives 0.129 N, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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Coulomb's Law and Force Between Point Charges

Two point charges \( 8 \times 10^{-7} \, \text{C} \) and \( -4 \times 10^{-7} \, \text{C} \) are 60 cm apart in vacuum.

**Inverse-square law** for charges states F ∝ 1/r² while increasing with charge product. Using k = 9×10⁹ N·m²/C², force at distance r follows F = k q₁q₂/r², forming basis for pairwise force calculation. Using Coulomb’s law: F = k (|q₁ q₂|/r²) . k = 9 × 10⁹ N·m²/C² , q₁ = 8 × 10⁻⁷ C , q₂ = -4 × 10⁻⁷ C , r = 0.6 m . |q₁ q₂| = 8 × 4 × 10⁻¹⁴ = 32 × 10⁻¹⁴ C² . r² = (0.6)² = 0.36 m² . F = 9 × 10⁹ × (32 × 10⁻¹⁴/0.36) = 9 × 10⁹ × 8.89 ×

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 \( +4 \, \mu\text{C}, -2 \, \mu\text{C}, +5 \, \mu\text{C} \) are at the vertices of an equilateral triang

**Independent action of charges** allows total force or field as vector sum. Geometry dictates distances to evaluation point, and resultant follows Σ k q_i/r_i², explaining zero field at symmetric centres for equal charges. F₁ = 9 × 10⁹ × (4 × 2 × 10⁻¹²/(1.2)²) = 0.05 N (attractive). F₂ = 9 × 10⁹ × (4 × 5 × 10⁻¹²/(1.2)²) = 0.125 N (repulsive). Angle 60°. Net F = √(F₁² + F₂² + 2 F₁ F₂ cos 60°) = √(0.05² + 0.125² + 0.00625) = 0.144 N . Substituting values gives 0.144 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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Superposition Principle and Equilibrium of Charges

Three charges \( +7 \, \mu\text{C}, -5 \, \mu\text{C}, +3 \, \mu\text{C} \) are at the vertices of an equilateral triang

**Superposition principle** asserts net Coulomb force on charge equals vector sum of forces from each other charge independently, F_net = Σ F_i, where F_i = k q q_i/r_i² r̂_i. In equilateral triangle or square symmetry, components may cancel at centroid, producing equilibrium. F₁ = 9 × 10⁹ × (7 × 5 × 10⁻¹²/(2)²) = 0.07875 N (attractive). F₂ = 9 × 10⁹ × (7 × 3 × 10⁻¹²/(2)²) = 0.04725 N (repulsive). Angle 60°. Net F = √(F₁² + F₂² + 2 F₁ F₂ cos 60°) = √(0.07875² + 0.04725² + 0.00372) = 0.098 N . Substituting values gives 0.098 N, which matches expected magnitude

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

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Superposition Principle and Equilibrium of Charges

Three charges \( +6 \, \mu\text{C}, -3 \, \mu\text{C}, +3 \, \mu\text{C} \) are at the vertices of an equilateral triang

**Superposition principle** asserts net Coulomb force on charge equals vector sum of forces from each other charge independently, F_net = Σ F_i, where F_i = k q q_i/r_i² r̂_i. In equilateral triangle or square symmetry, components may cancel at centroid, producing equilibrium. F₁ = 9 × 10⁹ × (6 × 3 × 10⁻¹²/1²) = 0.162 N (attractive). F₂ = 9 × 10⁹ × (6 × 3 × 10⁻¹²/1²) = 0.162 N (repulsive). Angle 60°. Net F = √(F₁² + F₂² + 2 F₁ F₂ cos 60°) = √(0.162² + 0.162² + 0.026244) = 0.28 N . Substituting values gives 0.28 N, which matches expected magnitude

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

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Coulomb's Law and Force Between Point Charges

Two point charges \( -3 \times 10^{-7} \, \text{C} \) and \( 5 \times 10^{-7} \, \text{C} \) are 80 cm apart in vacuum.

**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. Using Coulomb’s law: F = k (|q₁ q₂|/r²) . k = 9 × 10⁹ N·m²/C² , q₁ = -3 × 10⁻⁷ C , q₂ = 5 × 10⁻⁷ C , r = 0.8 m . |q₁ q₂| = 3 × 5 × 10⁻¹⁴ = 15 × 10⁻¹⁴ C² . r² = (0.8)² = 0.64 m² . F = 9 × 10⁹ × (15 × 10⁻¹⁴/0.64) = 9 × 10⁹ × 2.34375 × 10⁻¹³ = 0.00211

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

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