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Chapter 03 · Part V · Electromagnetism
Revised on ____________________
Chapter 03 · Moving Charges and Magnetism

A force that needs motion and never does work

2 sheets
2 diagrams
24 results

Formulas and conditions only — no derivations, no solved numbers. The diagrams are the reader's own.

I

The magnetic force

NO VELOCITY, NO FORCE
I.On a charge  F = q (v × B) zero if v ∥ B
II.Lorentz force  F = q (E + v × B)
III.Work done  zero, always speed never changes
IV.On a wire  F = I (L × B)
V.Radius  r = m vq B = √(2mK)/qB
VI.Period  T = 2π mq B no v in it — the cyclotron's secret
VII.Helical pitch  p = v∥ T
VIII.Velocity selector  v = EB undeflected beam
Same directionI₁I₂B₁B₂F→ ATTRACTOpposite directionI₁I₂F→ REPEL
II

Fields from currents

A WIRE FALLS AS 1/d, NOT 1/d²
I.Biot–Savart  dB = μ04π I dl × rr²
II.Long straight wire  B = μ0 I2π d circles the wire
III.Finite wire  B = μ0 I4π d (sin θ1 + sin θ2)
IV.Circular loop, centre  B = μ0 N I2 R
V.On its axis  B = μ0 N I R²2 (R² + x²)3/2
VI.Solenoid / toroid  B = μ0 n I , B = μ0 N I2π r
Ampère's law ∮B·dl = μ0 Ienc is always true, but it yields B only where symmetry lets you pull B outside the integral — solenoid, toroid, straight wire, sheet.
III

Currents on currents

LIKE CURRENTS ATTRACT
I.Between two wires  FL = μ0 I1 I22π d parallel attract, antiparallel repel
II.Magnetic moment  μ = N I A
III.Torque on a loop  τ = μ × B = N I A B sin θ θ from the normal, not the plane
IV.Energy  U = − μ·B least when aligned
V.Net force in a uniform field  zero torque without translation
VI.Orbiting electron  μ = e2m L the gyromagnetic ratio
BIFFμ = NIAθτ = NIAB sinθ — a couple, zero net force
IV

Instruments

ONE MOVEMENT, TWO METERS
I.Moving-coil deflection  θ = N I A Bk linear scale
II.Current sensitivity  N A Bk
III.Ammeter shunt  S = Ig GI − Ig
IV.Voltmeter series R  R = VIg − G
Permeability
μ0 = 4π×10−7
1 A at 1 m
B = 2×10−7 T
Earth's field
≈ 5×10−5 T
1 tesla
= 104 gauss
Cyclotron
f = qB / 2πm
Electron, e/m
1.76×1011 C kg−1
V

Where the marks go

FOUR ERRORS, EVERY YEAR
Where marks are lost in this chapter
1Expecting a force on a stationary charge. F = q(v × B) vanishes at v = 0 — ask for the velocity first.
2Letting a magnetic field speed a particle up. It is always ⊥ to v, so it does no work at all.
3Using the angle the coil's plane makes with B in τ = NIAB sin θ. θ is measured from the normal.
4Expecting parallel currents to repel by analogy with like charges. They attract — use the right-hand rule.