JEE/NEET Physics · Electromagnetic Induction series · Part 5 of 6 · All parts →
- Self-inductance L: a coil’s own changing current induces a BACK-EMF in itself
- ε = −L dI/dt; L depends only on geometry and core (solenoid: μ₀n²Al)
- Inductors store energy in fields: U = ½LI² — the magnetic cousin of ½CV²
- Mutual inductance M: one coil’s changing flux induces in a neighbour: ε₂ = −M dI₁/dt
- Henry (H): 1 H induces 1 V per amp-per-second change
A coil argues with itself: change its current and it induces a voltage opposing that very change — electrical inertia. Put a second coil nearby and they argue with each other — the transformer’s entire principle. Inductance is memory and conversation. Part 5 of the Electromagnetic Induction series.
- Self-inductance: electrical laziness
- The solenoid’s L
- Energy in the field
- Mutual inductance
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
Self-Inductance: Electrical Laziness
Current changes → its own flux changes → induced back-EMF opposes the change. A coil resists current CHANGES the way mass resists velocity changes: steady current flows freely; sudden switches spark and surge.
The Solenoid’s L
| Letter | What it means (plain words) | Value / unit |
|---|---|---|
| L | self-inductance | henry = V·s/A |
| M | mutual inductance between two coils | H |
| U | stored magnetic energy | U = ½LI² J |
Energy in the Field
Working against back-EMF while ramping current stores energy in the coil’s magnetic field: U = ½LI² — precisely the capacitor’s ½CV² with current for charge. Switch off, and the field returns the energy (as the spark across switches: inductance never forgets a debt).
Mutual Inductance
Coil 1’s current weaves flux through coil 2: change it and coil 2 feels EMF ε₂ = −M dI₁/dt. M depends on geometry and coupling — transformers, wireless chargers, and RFID cards are all M-conversations.
Solved Examples
|ε| = 2 × 3 = 6 V, opposing the change.
✔
Answer: 6 V
U = ½LI² = ½ × 2 × 16 = 16 J.
✔
Answer: 16 J
n = 2000/m; L = μ₀n²Al = 4π×10⁻⁷ × 4×10⁶ × 10⁻³ × 0.5 ≈ 2.5 mH.
Wind it on iron (μᵣ ~1000): henries — why transformers use iron cores.
✔
Answer: ≈2.5 mH (air)
- Inductance opposing current itself. It opposes CHANGES in current: steady DC flows unopposed (ideally).
- U = LI² (missing ½). The ramp is linear: average force half of final — the same ½ as springs and capacitors.
- M symmetrical? Yes: M₁₂ = M₂₁ always — a theorem worth remembering for tricky options.
- Iron core forgotten in solenoid L. μᵣ multiplies L by thousands: air-core formulas give answers thousands low on iron.
This Physics in Your Daily Life
- Every transformer on every pole — mutual inductance coupling coils on shared iron: voltage conversion by M.
- Spark plugs’ coils — collapsing field dumps ½LI² into a 20 kV spark: your car starting 50 times a day on stored field energy.
- Wireless chargers and RFID — loosely coupled mutual inductance across air gaps: cards and phones chatting by flux.
- Power supply smoothing chokes — self-inductance resisting current ripples: clean DC from noisy pulses: laziness as a feature.
- Nicola Tesla’s entire career — coils, resonance, and coupled inductors: the AC age built on this card.
Mass on wheels: hard to start, hard to stop — never resisting motion itself, only its change. An inductor is electrical inertia: the field it has built (or not) represents invested energy, and any current-change must reshape that investment. Sudden changes demand impossible energy rates — sparks and surges.
2 H coil ramped 0→4 A in 1 s: back-EMF 8 V fighting you throughout; at the end, 16 J sits in the field. Snap the switch: the same 16 J must exit instantly — a 2000 V spike across a 1 mm gap: stored energy doesn’t wait politely.
Graph current against time for a switch-on: instead of jumping, the current curves upward asymptotically (I(t) = I₀(1−e^(−t/τ))) — the inductor’s signature ‘reluctance curve’. Overlay voltage: a spike at switching, decaying to zero at steady state: the two pictures ARE the law.
Practice set (answers hidden — try first)
(NEET-level) L = 0.5 H, dI/dt = 4 A/s: |ε| =
(JEE Main-level) U for 10 A in 0.8 H:
(NEET-level) Inductor opposes
(Concept) Ideal inductor with steady DC: voltage across =
(JEE Main-level) Doubling turns density n of a solenoid: L
- ε = −L dI/dt: electrical inertia
- solenoid L = μ₀n²Al (geometry)
- U = ½LI² — field-stored energy
- mutual: ε₂ = −M dI₁/dt
- henry = V·s/A
- 🔁 self-inductance meaning
- 🔁 solenoid formula
- 🔁 energy storage
- 🧠 Chant: ‘coils hate change’.
- 🧠 Energy twin: ‘½LI² mirrors ½CV²’.
- 🏠 Daily: spark plugs fire on ½LI².
- 🏠 Daily: transformers converse through M.
Quick revision
- Self-inductance L: a coil’s own changing current induces a BACK-EMF in itself
- ε = −L dI/dt; L depends only on geometry and core (solenoid: μ₀n²Al)
- Inductors store energy in fields: U = ½LI² — the magnetic cousin of ½CV²
- Mutual inductance M: one coil’s changing flux induces in a neighbour: ε₂ = −M dI₁/dt
- Henry (H): 1 H induces 1 V per amp-per-second change
- Self-inductance: electrical laziness
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