Three long straight parallel wires carry currents as shown: Wire P: 3 A Wire Q: 1 A Wire R: 2 A Distance between adjacent wires: P–Q = 3 cm Q–R = 2 cm Find the net force per unit length on wire Q. Given: μ₀ = 4π × 10⁻⁷ T·m/A

Options: A) 6 × 10⁻⁷ N toward P B) 6 × 10⁻⁶ N toward R C) 6 × 10⁻⁷ N toward R D) 6 × 10⁻⁶ N toward P

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Solution

Force per unit length formula: F/L = (μ₀ I₁ I₂) / (2π d) Force due to P on Q: F₁ = (4π × 10⁻⁷ × 3 × 1) / (2π × 0.03) F₁ = (12 × 10⁻⁷) / (0.06) F₁ = 2 × 10⁻⁵ N/m Force due to R on Q: F₂ = (4π × 10⁻⁷ × 2 × 1) / (2π × 0.02) F₂ = (8 × 10⁻⁷) / (0.04) F₂ = 2 × 10⁻⁵ N/m Directions: Check current directions from diagram. Net force toward R. Correct Answer: B