Electromagnetic Principles: Basic laws of electromagnetism

Electromagnetic Principles: Basic laws of electromagnetism

1. What the Basic Laws Are (exam expects 4)

These are the foundations for understanding motors/generators/transformers:

Law	Equation / Statement	Meaning for Machines
Faraday's law of electromagnetic induction

(induced emf = -rate of change of flux linkage) ; Fleming's right-hand (generator) gives direction | Generator principle: moving conductor in $B$ ⇒ emf; Transformer $e∝dφ/dt$ |
| Lenz's law (sign) | Minus sign: induced current opposes change causing it | Ensures energy conservation |
| Ampère's circuital law (with Maxwell) |

; for solenoid

| Electromagnet field production |
| Fleming's left-hand (motor) / Lorentz force |

on conductor $l$ carrying $I$ in $B$ ; direction via left-hand (motor) | Motor principle: current in $B$ ⇒ force/torque |

Also Biot-Savart and B-H relation:

for magnetic circuit, reluctance

where

(magnetic Ohm's law, Hopkinson's law).

2. Why They Matter for Machines

• DC machine: Faraday generates $e$ in rotating armature, Lorentz produces torque $T∝φ I_a$.
• Transformer: Faraday $e = -N dφ/dt$ with $φ$ common to primary/secondary ⇒ voltage ratio.
• Induction motor: rotating $B$ from 3-phase induces $e$ in rotor ⇒ $I$ ⇒ force.

3. Worked Checks

(a) Coil N=100, φ changes 0.01 Wb in 0.1 s: e=-100·0.1= -10 V ✓

(b) Straight conductor l=0.1 m, B=1T, I=10A, θ=90°: F=1·10·0.1=1 N (motor force) ✓

(c) Solenoid n=1000/m, I=2A: H=2000 A/m, B=μ0 H=2.5 mT (air), φ= B·A

(d) Reluctance of iron core l=0.5 m, A=1e-4 m², μ_r=1000: R=0.5/(4πe-7·1000·1e-4)=3.98e6 A·t/Wb

4. Exam Points

• State Faraday $e=-N dφ/dt$ and Lenz sign — 5 marks, very frequent (almost certain to ask).
• State Ampère $∮ B·dl=μ_0 I$ and $B=μnI$ for solenoid — 5 marks, frequent.
• Give motor $F=BIl$ and generator $e=Blv$ — 5-7 marks, very frequent (most common machine principle question).
• Mention magnetic circuit $φ=NI/R$, $R=l/μA$ — 5 marks, frequent.