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Lesson 2: Mutual Induction Between Two Coils and Self-Induction of a Single Coil

Physics

Lesson 2: Mutual Induction Between Two Coils and Self-Induction of a Single Coil

Overview

Overview

🌳 Concept tree

  • Lesson 2 Mutual Induction Between Two Coils and Self-Induction of a Single Coil
  • ├── Mutual induction
  • ├── Self-induction
  • └── Eddy currents
Lesson 2: Mutual Induction Between Two Coils and Self-Induction of a Single Coil · 1 / 5
Mutual induction

Mutual induction

  • Place two coils near each other (or one inside the other) the primary, joined to a battery, switch and rheostat, and the secondary, joined to a sensitive galvanometer with a central zero.
  • A pointer deflection occurs in the secondary when:
  • the primary is brought close to (or pushed into) the secondary; the deflection is reversed when it is withdrawn;
  • the primary is inside the secondary and the current in the primary is increased (moving the rheostat); the deflection reverses when it is decreased;
  • the primary circuit is closed (current grows from zero); the deflection reverses when it is opened.
  • No deflection when the primary current is steady (the flux is not changing), and none when there is no current in the primary.
  • Interpretation when the primary current rises (or the primary approaches, or is switched on), the flux linked with the secondary rises and the induced current in the secondary is in the direction opposite to the primary current (its field opposes the increase).
  • When the primary current falls (or the primary is withdrawn, or is switched off), the induced current is in the same direction as the primary current (its field tries to maintain the flux).
  • This agrees with Lenz’s rule, and the experiment is also used to verify it.
  • Mutual induction is the production of an emf in one coil by a change of current in a neighbouring coil.
  1. The flux linked with the secondary is proportional to the primary current
  2. so the induced emf is proportional to the rate of change of the primary current:

emfsecondary = − M ΔIprimary / Δt

  • M is the coefficient of mutual induction (mutual inductance).
  • Its unit is the henry (H) = V·s/A.
  • A pair of coils has a mutual inductance of 1 H if an emf of 1 V is induced in the secondary when the current in the primary changes at 1 A/s.
  • The henry is the unit used to measure inductance in general.
  • M depends on the presence and type of an iron core inside the coils; the volume (size) of the coils and the number of their turns; the distance between them (and their relative orientation).
  • The transformer is a clear example of mutual induction, and the induction coil is another application.
  • Induction coil (brief):
  • a device with a primary of few thick turns around a soft-iron core and a secondary with very many thin turns.
  • An interrupter repeatedly breaks the DC in the primary; each break induces a very large emf in the secondary, giving a high voltage from a low-voltage battery (spark coils, ignition).
Lesson 2: Mutual Induction Between Two Coils and Self-Induction of a Single Coil · 2 / 5
Self-induction

Self-induction

  • Connect a coil with many turns and a soft-iron core (a strong electromagnet) in series with a 6 V battery and a switch.
  • While current flows, a strong magnetic field exists, and its flux links all the turns of the coil, since each turn acts as a small magnet.
  • When the switch is opened, the current drops to zero very quickly. The magnetic field of the neighbouring turns falls to zero, so each turn cuts the diminishing flux lines and an emf is induced in the same coil. By Lenz’s rule it is in the direction of the original current, trying to keep it flowing.
  • Because the coil has many turns and the current falls so fast, this induced emf is much larger than the battery’s emf. A spark jumps across the switch contacts, and a neon lamp (needing about 180 V) connected across the switch glows.
  • When the switch is closed, the induced emf opposes the growth of the current, so the current in the coil rises slowly to its final value.
Self-induction→the production of an emf in a coil by a change of the current in the same coil; the induced emf opposes the change.

emf = − L ΔI / Δt

Comparison aspectMain ideaKeywords
L is the coefficient of self-induction (self inductance)
  • the emf induced in the coil when the current changes at the rate of 1 A/s. Unit: henry — the self inductance of a coil in
  • an emf of 1 V is induced when the current through it changes at the rate 1 A/s (1 H = 1 V·s/A)
inducedcoilcurrentchanges
L depends on
  • the geometry (shape and size) of the coil
  • the number of turns
  • the spacing of the turns
  • and the permeability of the core (an iron core greatly increases L)
geometryshapesizecoil
•Applications/notesApplicationsnotes
  • Starting a fluorescent lamp (choke/ballast) the large self-induced emf on interrupting the current produces the high voltage that ignites the lamp, and the choke limits the current afterwards.
  • Resistance coils (rheostat boxes) are wound with double (bifilar) wire — the wire is folded in the middle and wound so that the currents in adjacent turns are opposite. Their magnetic fields cancel and the self-inductance is practically zero, so the coil acts as a pure resistance and no sparks occur at make/break. For the same reason an iron bar inside such a coil is not magnetized.
  • The current in a coil with an iron core dies out more slowly than in an air-core coil, and the current in an air-core coil dies out more slowly than in a straight wire, because of the larger self-induced emf. The same is true for the rise of the current.
Comparison aspectMain ideaKeywords
Example 3.The current in a coil falls from 4 A to 0 in 0.02 s and the induced emf is 20 V. L = 20 × 0.02/4 = 0.1 Hcurrentcoilfallsinduced
Example 4.Two coils have M = 0.2 H. The primary current changes from 3 A to 0 in 0.05 s. emf = 0.2 × 3/0.05 = 12 V in the secondarycoilsprimarycurrentchanges
Example 4a — self-induction.A coil of L = 0.8 H has its current raised uniformly from 0 to 2.5 A in 0.5 s. The rate of change is 5 A/s and the opposing emf is 0.8 × 5 = 4 Vcoilcurrentraiseduniformly
Example 4b — finding M.
  • While the current in a primary coil changes uniformly from 1 A to 7 A in 0.06 s
  • an emf of 15 V is induced in the secondary. M = emf × Δt / ΔI = 15 × 0.06 / 6 = 0.15 H
Whilecurrentprimarycoil
Lesson 2: Mutual Induction Between Two Coils and Self-Induction of a Single Coil · 3 / 5
Eddy currents

Eddy currents

  • When the flux through a piece of solid metal changes with time, closed induced currents circulate inside the metal in closed paths.
  • These are eddy currents.
  • The change in flux is produced either by moving the solid in a suitable magnetic field or by placing it in an alternating field (for example the field of an AC current).
  • They produce heating. Useful: induction furnaces that melt metals.
  • Harmful in transformer and motor cores (waste of energy as heat); reduced by using a laminated core, thin insulated sheets with high resistivity.
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Lesson 2: Mutual Induction Between Two Coils and Self-Induction of a Single Coil · 4 / 5
Part 5

Part 5

  • 📖

🔍 In-Depth Explanations, Deductions & Multi-Book Insights:

Physics (Thanaweya Amma 2026/2027)

  • Lesson 2 – Mutual Induction Between Two Coils and Self-Induction of a Single Coil
  • Mutual induction occurs when changing current in a primary coil induces an EMF in an adjacent secondary coil.
  • Self-induction occurs within a single coil as its own changing current creates a back-EMF opposing the original current change.

🌳 Conceptual Hierarchy Tree

Mutual and Self Induction Mechanics

├── 1. Mutual Induction (Coefficients M)

│ ├── emf2 = -M · (ΔI1 / Δt) = -N2 · (ΔΦm2 / Δt)
│ ├── Forward induced EMFGenerated during opening of primary circuit or decreasing current (Reinforcing)
│ └── Backward induced EMFGenerated during closing of primary circuit or increasing current (Opposing)

└── 2. Self-Induction (Coefficient L)

├── emf = -L · (ΔI / Δt) = -N · (ΔΦm / Δt)
├── Henry (H)Unit of inductance (H = V·s/A = Ω·s = Wb/A)
├── Self-Inductance formulaL = (μ · N2 · A) / l
└── Eddy CurrentsInduced circular currents in solid iron cores causing heating; minimized by laminating cores into insulated sheets

📋 Master Teacher's Blackboard Secrets

Comparison aspectMain ideaKeywords
RULE 1At the moment of opening an inductive circuit: A tremendous FORWARD induced EMF is generated (spanning thousands of volts) causing an electrical spark across the switch terminalsmomentopeninginductivecircuit
RULE 2To make a non-inductive resistance (wound coil with zero self-induction): The wire is doubly wound (bifilar winding) so the magnetic fields of equal and opposite currents cancel outmakeinductiveresistancewound
RULE 3
  • Self-inductance L is proportional to the SQUARE of turns (N2): If turns are doubled with same length
  • L quadruples!
SelfinductanceproportionalSQUARE
EXAM TRAPInduction furnaces melt metals using Eddy currents generated by high-frequency alternating magnetic fieldsInductionfurnacesmeltmetals
📊 MatrixComparative Synthesis: Backward vs. Forward Induced EMFComparativeSynthesisBackwardForward
Feature Backward Induced EMF (emf_back) Forward Induced EMF (emf_forward)
Triggering Cause
  • Increasing current (Closing circuit
  • decreasing rheostat)
  • Decreasing current (Opening circuit
  • increasing rheostat)
Relative Direction Opposes applied battery current In same direction as battery current (Reinforces)
Magnitude Smaller (growth of current is gradual) Extremely large (decay of current is instantaneous)
Physical Consequence Delays current from reaching maximum steady state Produces electric spark across open switch terminals
Lesson 2: Mutual Induction Between Two Coils and Self-Induction of a Single Coil · 5 / 5