Electromagnetic Induction

Number of turns, Cross-sectional area, Length of solenoid, Permeability of core material

Self-inductance L = μ₀n²Al = μ₀N²A/l, where N is number of turns, A is area, l is length, and μ₀ is permeability. Current does not affect inductance as it's a property of the geometry and material.

Henry

The unit of inductance is Henry (H), named after Joseph Henry. 1 H = 1 V·s/A = 1 Ω·s. Weber is the unit of magnetic flux, Tesla is for magnetic field, and Farad is for capacitance.

6.28 mH

For a solenoid: L = μ₀N²A/l. Given: N = 500, A = 0.01 m², l = 0.5 m, μ₀ = 4π × 10⁻⁷ H/m. L = (4π × 10⁻⁷ × 500² × 0.01)/0.5 = 6.28 × 10⁻³ H = 6.28 mH

9 J

Energy stored in an inductor: U = ½LI². Given: L = 2 H, I = 3 A. Therefore, U = ½ × 2 × 3² = ½ × 2 × 9 = 9 J