Self-Inductance of SolenoidMediumQuestion 20219
Question
A solenoid has 2000 turns, length 50 cm, and cross-section 4 cm². Its self-inductance (μ₀ = 4π×10⁻⁷) is:
- A4π×10⁻³ HCorrect
- B4π×10⁻⁴ H
- C8π×10⁻³ H
- D2π×10⁻³ H
Correct answer
4π×10⁻³ H
Explanation
n = 2000/0.5 = 4000 /m. A = 4×10⁻⁴ m². L = μ₀n²Al = 4π×10⁻⁷ × 16×10⁶ × 4×10⁻⁴ × 0.5 = 4π×10⁻⁷ × 16×10⁶ × 2×10⁻⁴ = 4π×10⁻⁷ × 3200 = 4π × 3.2×10⁻⁴ ≈ 4.02×10⁻³ H ≈ 4π×10⁻³ H... Recompute: L = μ₀N²A/l = 4π×10⁻⁷ × (2000)² × 4×10⁻⁴ / 0.5 = 4π×10⁻⁷ × 4×10⁶ × 8×10⁻⁴ = 4π×10⁻⁷ × 3200 = 4π×3.2×10⁻⁴ ≈ 4.02×10⁻³ H ≈ 4π×10⁻³ H.