Engine of Electromagnetism

NODE 01

Discovery of Induction

N

S

• Can magnetism produce electricity? Yes.
• A changing magnetic environment induces EMF.
• Crucial word: CHANGE.

NODE 02

Magnetic Flux

• Φ_B = BA cosθ.
• Field, Area, Orientation.
• Changing flux → induced EMF.

NODE 03

Changing Flux

ΔBΔAΔθ

• Change field strength (B).
• Change loop area (A).
• Change orientation (θ).

NODE 04

Faraday's Law

ε=-NdΦ/dt

• ε = -N dΦ_B/dt.
• Induced EMF depends on rate of flux change.
• Negative sign represents opposition.

NODE 05

Lenz's Law

• Induced effect opposes the change in flux.
• Change → Induction → Opposition.
• Expression of Energy Conservation.

NODE 06

Lenz: Mag & Coil

N

S

• Move mag toward coil → resists increase.
• Move mag away → resists decrease.
• Direction of motion matters.

NODE 07

Induced Current

I=ε

R

• Closed circuit: EMF drives current (I = ε/R).
• Stronger from: faster change, more turns, stronger B.

NODE 08

Open vs Closed

• Open: EMF exists, but I = 0.
• Closed: EMF drives induced current.

NODE 09

Motional EMF

• Conductor moving through B-field.
• ε = BLv.
• Produces charge separation.

NODE 10

How Motional Arises

• Moving charges inside rod feel magnetic force.
• Causes charge separation → EMF.
• Connects Realm 18 to 19.

NODE 11

RHR for Motional

• v × B gives force on positive charge.
• Determines which end is higher potential.

NODE 12

Moving Rod on Rails

• Changing loop area → changing flux → EMF → Current.
• Current experiences force opposing motion (Lenz).

NODE 13

Energy Cons in Ind

MECH WORK↓ELEC ENERGY↓THERMAL E

• Opposing force means external work is needed.
• Work → Electrical Energy → Thermal Energy.

NODE 14

Generator Concept

• Mechanical motion continuously changes flux.
• Mech Energy → Electrical Energy.

NODE 15

AC Generator Intro

• Coil rotating in magnetic field.
• Continuous change in Φ → Alternating EMF.

NODE 16

Sinusoidal EMF

• ε = ε₀ sin(ωt) where ε₀ = NBAω.
• Bridge to Realm 20 (AC Circuits).

NODE 17

Generator Freq

f=ω/2π

• Mechanical rotation speed determines electrical frequency.

NODE 18

Dynamo / Generator

MECH

ELEC

• Converts Mech E to Elec E.
• Driven by turbine, wind, steam, etc.

NODE 19

Transformers Intro

• Changing I → Changing B → Changing Φ → Induced EMF.
• Mutual induction between coils.

NODE 20

Self-Induction

• Changing current in a coil changes its OWN flux.
• Induces EMF opposing the current change.
• ε = -L dI/dt (Electrical inertia).

NODE 21

Inductance (L)

L

• How strongly a circuit opposes current change.
• Unit: henry (H).

NODE 22

Flux Linkage

NΦ=LI

• For an N-turn coil: flux linkage = NΦ.
• Linear case: NΦ = LI.

NODE 23

Solenoid L

μN²A

l

• L = μN²A/l.
• Geometry and core material determine inductance.

NODE 24

Mutual Inductance

• Current change in coil 1 induces EMF in coil 2.
• ε₂ = -M dI₁/dt. M = Mutual inductance.

NODE 25

Coupled Coils

• Primary/Secondary coils, magnetic coupling.
• Shared flux via core. Architecture of transformers.

NODE 26

Transformer Princ

V_sN_s

V_pN_p

• Ideal transformer: V_s / V_p = N_s / N_p.
• Voltage transformation via turns ratio.

NODE 27

Step-Up

• N_s > N_p → V_s > V_p.
• Used in high-voltage transmission.

NODE 28

Step-Down

• N_s < N_p → V_s < V_p.
• Power supplies, household appliances.

NODE 29

Transformer Power

V_pI_p=V_sI_s

• Ideal power is conserved.
• Voltage ↑ means Current ↓ (and vice versa).

NODE 30

Why Trans Need AC

X

✓

• Requires continually changing magnetic flux.
• DC produces steady field (no induction after transients).

NODE 31

Transformer Losses

RESISTEDDYHYSTERLEAK

• Real transformers lose energy.
• Coil resistance, eddy currents, hysteresis, leakage.

NODE 32

Eddy Currents

• Changing B-field induces circulating currents in conductors.
• Causes heating/loss, but useful for braking/heating.

NODE 33

Eddy Reduction

• Laminated cores (thin insulated layers).
• Increases resistance to large current loops → reduces loss.

NODE 34

Hysteresis Loss

• Repeated magnetization in AC dissipates energy.
• Connects to Realm 17 (Magnetic Materials).

NODE 35

Inductor

• Circuit element exhibiting significant inductance.
• Opposes current change, stores magnetic energy.

NODE 36

Energy Stored

U=½LI²

• Magnetic-field energy storage.
• Parallel to capacitor's electric-field energy.

NODE 37

Cap vs Inductor

CAP (E)IND (B)

Opposes ΔVOpposes ΔI

U=½CV²U=½LI²

• Perfect symmetric duality. Critical for Realm 20.

NODE 38

LC Oscillation

• Energy oscillates between Electric (C) and Magnetic (L) fields.
• An electrical oscillator.

NODE 39

EM Oscillation

ω=1/√(LC)

• Ideal LC angular frequency.
• Bridge: mechanical oscillator ↔ electrical oscillator.

NODE 40

Motors & Generators

ELEC→ MOTOR →MECH

MECH→ GEN →ELEC

• Closely related electromagnetic machines.
• Reverse relationships.

NODE 41

Braking by Induction

• Changing B-field → induced current opposes motion.
• Eddy-current brakes, magnetic damping.

NODE 42

Induction Heating

• AC magnetic fields induce heating currents in metals.
• Induction cooktops, industrial metal processing.

NODE 43

Wireless Power

• Time-varying EM fields transfer energy between coupled coils.
• Resonant coupling.

NODE 44

EM Ind in Nature

🌍☀️⚡

• Earth's changing magnetic environment.
• Geomagnetically induced currents, solar activity.

NODE 45

Experiment Lab

MAG+COILSPEEDTURNSB-FIELD

• Move magnet in/out of coil. Compare speed/turns/field.
• Observe self/mutual induction, transformer ratios.

NODE 46

Graph Chamber

• ε ∝ -dΦ/dt. ε ∝ v.
• Transformer V ∝ N. Inductor ε ∝ -dI/dt.

NODE 47

Misconceptions

X

• "B-field induces electricity" → Requires CHANGING flux.
• "Lenz violates motion" → It's energy conservation.
• "Transformers work on DC" → Only during transients.

NODE 48

Solving Engine

• Find Φ → What is changing (B, A, θ)?
• Calc ΔΦ/Δt → ε = -N dΦ/dt → Lenz for dir.
• Motional (BLv), Self (-L dI/dt), Mutual (-M dI/dt).

NODE 49

Master Map

FLUX → CHANGE → EMFFARADAY → LENZ → CURRENTMOTIONAL / SELF / MUTUAL

• The entire realm compressed.

NODE 50

Deep Synthesis

E↔B

• R15: Charge → E-field. R16: Flow → Current.
• R17: Current → B-field. R18: B-field → Force.
• R19: Changing B-field → E-field (EMF).
• Electricity creates magnetism. Magnetism creates electricity.