The Magnetic Dance

NODE 01

The Magnetic Force

F = q(v × B)

• F = qvB sinθ.
• Force on a moving charged particle.
• Depends on charge, velocity, field, and angle.

NODE 02

When Force is Zero

v=0B=0θ=0°θ=180°

• Stationary charge (v=0).
• No field (B=0).
• Velocity parallel/antiparallel to field.

NODE 03

Right-Hand Rule

• v × B → F (for positive charge).
• Negative charge: force direction reverses.

NODE 04

Mag Force Does No Work

F⊥v∴ W=0

• Force is perpendicular to instantaneous velocity.
• Changes direction, NOT kinetic energy.
• Particles curve without speeding up.

NODE 05

Entering B Field

• v ⊥ B → Circular path.
• v ∥ B → Straight line.
• Angle → Helical path.

NODE 06

Circular Motion

• Magnetic force provides centripetal force.
• qvB = mv²/r → r = mv/(|q|B).

NODE 07

Angular Frequency

ω_c=|q|B/m

• Cyclotron angular frequency.
• Non-relativistic ideal case: independent of speed!

NODE 08

Time Period

2πm

|q|B

• T = 2πm/(|q|B).
• f = |q|B/(2πm).
• Mass spectrometry, cyclotron.

NODE 09

Helical Motion

• Velocity has parallel (v∥) and perp (v⊥) components.
• v∥ is constant, v⊥ makes a circle.
• Combined = Helix.

NODE 10

Pitch of the Helix

• Distance advanced along field in one revolution.
• Pitch = v∥T.
• Combines linear and circular motion.

NODE 11

Force on Conductor

F=BIL

• F = I(L × B). Mag: F = BIL sinθ.
• Connects individual charge picture to circuits.

NODE 12

Current Loop

• Behaves as a magnetic dipole (μ = IA).
• Torque: τ = μB sinθ.
• Connects to Realm 05 (Torque).

NODE 13

Galvanometer

• Current → Mag Torque → Coil rotates → Deflection.
• Measurement technology.

NODE 14

Galvanometer Princ

τ_mag=τ_spring

• Equilibrium: Mag torque = Restoring torque.
• Deflection ∝ Current.

NODE 15

Conversion to Ammeter

• Add suitable shunt resistance in parallel.
• Allows large current to bypass sensitive coil.

NODE 16

Conversion to Voltmeter

• Add large series resistance.
• Draws little current while measuring PD.

NODE 17

Mag Torque & Eq

• Stable/Unstable orientation.
• Meeting point of Current + Field + Rot Dynamics.

NODE 18

Lorentz Force

F=q(E+v×B)

• Combines Electric (qE) and Magnetic (q(v×B)) forces.
• The core equation of the EM universe.

NODE 19

E + B Fields

• Electric acceleration + Magnetic deflection.
• Opens the door to charged-particle control.

NODE 20

Velocity Selector

• E and B forces oppose: qE = qvB.
• Only v = E/B passes undeflected.

NODE 21

Mass Spectrometry

• Velocity-selected particle bent by B-field.
• r = mv/qB gives mass-to-charge info.

NODE 22

Cyclotron

• Electric accel + Magnetic bending + Repeated accel.
• Cyclotron frequency, particle energy.

NODE 23

Hall Effect

• Charge carriers deflected sideways.
• Produces a transverse voltage.

NODE 24

Hall Voltage

ΔVH

• B-field + Current → Charge Imbalance → Voltage.
• Mag sensors, carrier sign/density.

NODE 25

Earth's B-Field (Part)

• Solar wind, particle trapping.
• Magnetosphere. Bridge to space Physics.

NODE 26

Aurorae

• Particles guided by B-field hit upper atmosphere.
• Excited atoms → light.

NODE 27

Particle Traps

• Magnetic confinement, Penning trap.
• Cyclotron motion, guiding centres.

NODE 28

Plasma Motion

• Ions/Electrons influenced by EM fields.
• Magnetic confinement, plasma oscillations.

NODE 29

Magnetic Mirror

• Varying B-field → pitch-angle change → reflection.
• Plasma confinement, space physics.

NODE 30

Drift of Particles

• Non-uniform/crossed fields → drift motions.
• E×B drift, Gradient-B drift, Curvature drift.

NODE 31

E × B Drift

v_drift=E×B/B²

• Uniform crossed fields.
• Collective drift independent of charge sign.

NODE 32

Magnetic Moment

• Circulating charge = magnetic dipole.
• Bridge into atomic Physics.

NODE 33

Force & Work Dist

F_elecW ≠ 0

F_magW = 0

• Electric force: Changes KE (does work).
• Mag force: Perpendicular to v, does NO work.

NODE 34

Instruments

G

A

V

H

• Galvanometer, Ammeter, Voltmeter.
• Hall sensor, Fluxmeter.

NODE 35

Mag Force Exp

F ∝ IF ∝ BF ∝ LF ∝ sinθ

• Plotting force vs current, field, length, angle.

NODE 36

Particle Exp

r ∝ vr ∝ 1/Br ∝ mr ∝ 1/|q|

• Turning Lorentz-force equations into measurable relationships.

NODE 37

Galvanometer Lab

• Determine current sensitivity, measure resistance.
• Convert to ammeter/voltmeter, calibrate scales.

NODE 38

Vis Chamber

• Interactive cases: v → B → F.
• Change charge sign, observe force reversal.

NODE 39

Graph Chamber

• F vs I (Linear), r vs v (Linear).
• Hall voltage vs B (Linear).

NODE 40

Misconceptions

X

• "B-field does work" → No, F is perp to v.
• "Stationary charge feels mag force" → No.
• "Pos/Neg bend same way" → Opposite directions.

NODE 41

Solving Engine

• ID q, v, B → Check angle → F = qvB sinθ.
• F ⊥ v? → KE const → qvB = mv²/r.
• For conductor: F = BIL sinθ.

NODE 42

Master Map

MOVING CHRG → B-FIELDLORENTZ F → CIRC/HELIXCOND/LOOP → F/τ → GALV

• The complete architecture of the Magnetic Dance.

NODE 43

Deep Synthesis

• R15: Charge → E-field. R16: Moving charge → Current.
• R17: Current → B-field. R18: B-field → Force on moving charge.
• Charge produces & experiences EM effects.