A 0.5m long solenoid of 10 turns/cm has area of cross-section 1cm². Calculate the voltage induced across its ends if the current in the solenoid is charged from 1A to 2A in 0.1s.

emf included in a coil is emf = −LΔI/ΔT
Now;
ΔI = 2A − 1A
ΔT = 0.1sec
∴ ΔI/ΔT = 10/1 = 10
L = μ₀N²A/l, μ₀ = 4π × 10⁻⁷
N = 50cm × 10 turns/cm
N = 500 turns
A = area of cross section = 1cm² = 10⁻⁴m²
l = length of the coil = 0.5m
∴L = 4π × 10⁻⁷ × (5 × 10²)² × 10⁻⁴ / 0.5 = 4π × 10⁻⁷ × 25 × 10⁴ × 10⁻⁴ / 0.5 = 6.28 × 10⁻³
∴emf induced = 6.28 × 10⁻³ × 10 = 6.28 × 10⁻² volts