#dipole torque

Electric Dipole - Moment, Field and Torque

A dipole with charges \( +6 \, \mu\text{C} \) and \( -6 \, \mu\text{C} \) separated by 4 mm is in a field \( 5 \times 10

**Dipole moment** governs torque and energy in external field. Axial field stronger than equatorial, torque maximum at θ = 90°, zero when aligned. Work done rotating dipole relates to ΔU = pE(1 - cosθ), explaining stable equilibrium at θ = 0°. Dipole moment: p = q × 2a = 6 × 10⁻⁶ × 4 × 10⁻³ = 2.4 × 10⁻⁸ C m . Torque: tau = p E sin θ = 2.4 × 10⁻⁸ × 5 × 10⁴ × sin 60° = 1.2 × 10⁻³ × (√(3)/2) = 1.04 × 10⁻³ N m . Substituting values gives 1.04 × 10⁻³ N m, which matches expected

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Electric Dipole - Moment, Field and Torque

A dipole with \( p = 4 \times 10^{-9} \, \text{C m} \) is at 30° to a field \( E = 6 \times 10^4 \, \text{N/C} \). What

**Interaction of dipole with uniform field** produces pure couple without net force, equal opposite forces forming torque. Potential energy minimum -pE at alignment, maximum +pE at anti-alignment, governing orientation dynamics. tau = p E sin θ . tau = 4 × 10⁻⁹ × 6 × 10⁴ × sin 30° = 24 × 10⁻⁵ × 0.5 = 1.2 × 10⁻⁴ N m . Substituting values gives 1.2 × 10⁻⁴ N m, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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Electric Dipole - Moment, Field and Torque

A dipole with charges \( +5 \, \mu\text{C} \) and \( -5 \, \mu\text{C} \) separated by 3 mm is in a field of \( 2 \times

**Interaction of dipole with uniform field** produces pure couple without net force, equal opposite forces forming torque. Potential energy minimum -pE at alignment, maximum +pE at anti-alignment, governing orientation dynamics. Dipole moment: p = q × 2a = 5 × 10⁻⁶ × 3 × 10⁻³ = 1.5 × 10⁻⁸ C m . Torque: tau = p E sin θ = 1.5 × 10⁻⁸ × 2 × 10⁴ × sin 45° = 3 × 10⁻⁴ × (√(2)/2) = 2.12 × 10⁻⁴ N m . Substituting values gives 2.12 × 10⁻⁴ N m, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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Electric Dipole - Moment, Field and Torque

A dipole with charges \( +3 \, \mu\text{C} \) and \( -3 \, \mu\text{C} \) separated by 5 mm is in a field \( 8 \times 10

**Dipole moment** governs torque and energy in external field. Axial field stronger than equatorial, torque maximum at θ = 90°, zero when aligned. Work done rotating dipole relates to ΔU = pE(1 - cosθ), explaining stable equilibrium at θ = 0°. Dipole moment: p = q × 2a = 3 × 10⁻⁶ × 5 × 10⁻³ = 1.5 × 10⁻⁸ C m . Torque: tau = p E sin θ = 1.5 × 10⁻⁸ × 8 × 10⁴ × sin 45° = 1.2 × 10⁻³ × (√(2)/2) = 8.48 × 10⁻⁴ N m . Substituting values gives 8.48 × 10⁻⁴ N m, which matches expected

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Electric Dipole - Moment, Field and Torque

A dipole with \( p = 7 \times 10^{-9} \, \text{C m} \) is at 45° to a field \( E = 9 \times 10^4 \, \text{N/C} \). What

**Electric dipole** consists of charges +q and -q separated by 2a, dipole moment p = q·2a, vector from negative to positive, unit C·m. In uniform field E, torque τ = p × E, magnitude τ = p E sinθ, tending to align p with E, potential energy U = -p·E = -p E cosθ. tau = p E sin θ . tau = 7 × 10⁻⁹ × 9 × 10⁴ × sin 45° = 63 × 10⁻⁵ × (√(2)/2) = 4.45 × 10⁻⁴ N m . Substituting values gives 4.45 × 10⁻⁴ N m, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and

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Electric Dipole - Moment, Field and Torque

A dipole with \( p = 6 \times 10^{-9} \, \text{C m} \) is at 60° to a field \( E = 3 \times 10^4 \, \text{N/C} \). What

**Dipole moment** governs torque and energy in external field. Axial field stronger than equatorial, torque maximum at θ = 90°, zero when aligned. Work done rotating dipole relates to ΔU = pE(1 - cosθ), explaining stable equilibrium at θ = 0°. tau = p E sin θ . tau = 6 × 10⁻⁹ × 3 × 10⁴ × sin 60° = 18 × 10⁻⁵ × (√(3)/2) = 1.56 × 10⁻⁴ N m . Substituting values gives 1.56 × 10⁻⁴ N m, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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Electric Dipole - Moment, Field and Torque

A dipole with charges \( +2 \, \mu\text{C} \) and \( -2 \, \mu\text{C} \) separated by 1 mm is in a field of \( 6 \times

**Dipole moment** governs torque and energy in external field. Axial field stronger than equatorial, torque maximum at θ = 90°, zero when aligned. Work done rotating dipole relates to ΔU = pE(1 - cosθ), explaining stable equilibrium at θ = 0°. Dipole moment: p = q × 2a = 2 × 10⁻⁶ × 1 × 10⁻³ = 2 × 10⁻⁹ C m . Torque: tau = p E sin θ = 2 × 10⁻⁹ × 6 × 10⁴ × sin 90° = 1.2 × 10⁻⁴ N m . Substituting values gives 1.2 × 10⁻⁴ N m, which matches expected magnitude for this electrostatic configuration, confirming

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