An air-cored solenoid with length 30 cm, area of cross-section 25 cm² and number of turns 500 carries a current of 2.5 A. The current is suddenly switched off in a brief time of 10⁻³ s. How much is the average back emf induced across the ends of the open switch in the circuit? Ignore the variation…

Question

An air-cored solenoid with length 30 cm, area of cross-section 25 cm² and number of turns 500 carries a current of 2.5 A. The current is suddenly switched off in a brief time of 10⁻³ s. How much is the average back emf induced across the ends of the open switch in the circuit? Ignore the variation in magnetic field near the ends of the solenoid.

Accepted Answer

(1) 6.54 V. Given: ℓ = 30 cm = 0.30 m, A = 25 cm² = 25×10⁻⁴ m², N = 500; the current falls from 2.5 A to 0 in Δ t = 10⁻³ s. Idea: find the self-inductance of the solenoid first, then use |ε| = L(Δ I)/(Δ t). L = (μ₀N²A)/ℓ = (4π×10⁻⁷×(500)²×25×10⁻⁴)/(0.30) ≈ 2.618×10⁻³ H. Average back emf: |ε| = 2.618×10⁻³×(2.5)/(10⁻³) ≈ 6.54 V.

Step-by-step solution

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