Inductance
Self-induction: when the current in a coil changes, the flux linked with the same coil changes, and an emf is induced in it which opposes the change in current. Flux linkage NΦ = LI, where L is the self-inductance. The induced emf is ε = –L dI/dt. Unit of inductance: henry (H) = V s/A.
Self-inductance acts like inertia for current: it opposes both a rise and a fall in current. This opposing emf is called back emf.
For a long solenoid of N turns, length l and area A: L = μ₀N²A/l = μ₀n²Al. With a core of relative permeability μ_r, L becomes μ_r times larger.
Energy stored in an inductor: U = ½LI². This energy is stored in the magnetic field.
Mutual induction: when the current in one coil changes, an emf is induced in a nearby coil. N₂Φ₂ = M I₁ and ε₂ = –M dI₁/dt. M is the mutual inductance; it depends on the shapes, sizes, number of turns, separation and orientation of the coils and on the core material. For two long coaxial solenoids, M = μ₀n₁n₂Al. Mutual induction is the working principle of the transformer.
Worked example: a 0.2 H coil carries 5 A, which falls to zero in 0.1 s. Average emf = 0.2 × 5/0.1 = 10 V. Energy initially stored = ½ × 0.2 × 25 = 2.5 J.
Key points
- ε = –L dI/dt; ε₂ = –M dI₁/dt.
- L = μ₀N²A/l for a solenoid (∝ N²).
- U = ½LI².
- 1 H = 1 V s A⁻¹.
Exam tips
- Doubling the turns of a solenoid (same length and area) makes L four times.
- Inductance is like mass, current like velocity: compare ½LI² with ½mv².
Common mistakes
- Thinking L depends on the current; it depends only on geometry and core.
- Confusing self-inductance with resistance.
- Forgetting that M depends on orientation of the coils.