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What is the self-inductance of a solenoid of length 31.4 cm, area of cross-section 10⁻³ m² and total number of turns 10³?

Asked in GUJCET 2011 · Coil geometry, cores and combinations

• (1) 4 mH
• (2) 4 H
• (3) 40 H
• (4) 0.4 H

Step-by-step solution

Why the other options are wrong

• (2) 4 H drops the 10⁻³ of the area, that is, it uses A = 1 m²: (4π×10⁻⁷ × 10⁶ × 1)/(0.314) = 4.
• (3) No single slip gives 40 H. Sanity check: (μ₀N²A)/l = (4π×10⁻⁷ × 10⁶ × 10⁻³)/(0.314) = 4×10⁻³ H, ten thousand times smaller.
• (4) No single slip gives 0.4 H; it is 100 times the correct 4×10⁻³ H. Check the powers of ten: 4π×10⁻⁷ × 10⁶ × 10⁻³ = 4π×10⁻⁴.

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