Magnetism ↔ Current Electricity (Chapter before)
- Ohm's law gives I → Biot-Savart gives B from I → Ampere gives ∮B·dl = μ_{0}I
- Galvanometer conversion uses: V = IR (Ohm's law) + F = NIAB (magnetic torque)
- Parallel wire force defines the ampere — the base SI unit of current
Magnetism ↔ Electromagnetic Induction (Next chapter)
- A changing magnetic flux induces EMF: ε = −dΦ/dt (Faraday's law)
- The same B field that exerts force on charges here creates EMF when it changes
- Lenz's law (opposing induced current) is the reverse of the force relationship here
- Key link: The magnetic moment M = NIA of a coil appears in both torque (τ = MB sinθ) and in the expression for induced EMF in a rotating coil
Magnetism ↔ Modern Physics
- Cyclotron uses T = 2π → velocity selector concept → mass spectrometry → isotope separation
- Electron spin is a quantum magnetic moment → explains paramagnetism and ferromagnetism at the atomic level
- Bohr magneton: μ_B = eℏ/(2) — fundamental unit of atomic magnetic moment
Magnetism ↔ Electrostatics (Contrast table)
| Feature | Electric Field E | Magnetic Field B |
|---|---|---|
| Source | Stationary charges (Coulomb) | Moving charges / currents (Biot-Savart) |
| Force on test charge | F = qE (along E) | F = qv×B (⊥ to v and B) |
| Work done | Can do work (F along displacement possible) | Never does work (F ⊥ v always) |
| Field lines | Start on +q, end on −q (open lines) | Always closed loops (no monopoles) |
| Gauss's law analog | ∮E·dA = /ε_{0} | ∮B·dA = 0 (no monopoles) |