Magnetism and Magnetic Effects of Electric Current
This domain links magnetic fields to currents and moving charges: the Biot–Savart law, Ampere's law, force on charges and conductors, torque on a current loop, and the moving-coil galvanometer with its ammeter and voltmeter conversions.
Core rules
- Biot–Savart: dB = (μ₀/4π)(I dl sin θ)/r², with μ₀/4π = 10⁻⁷ T m A⁻¹.
- Long straight wire: B = μ₀I/(2πr). Centre of a circular coil: B = μ₀NI/2R. Long solenoid: B = μ₀nI, n being turns per metre. Toroid: B = μ₀NI/(2πr).
- Force on a charge F = qvB sin θ, perpendicular to both v and B; on a conductor F = BIl sin θ. The magnetic force does no work, so kinetic energy is unchanged.
- Torque on a coil τ = NIAB sin θ, with θ measured between the coil normal and B; maximum when the coil plane is parallel to the field.
- Moving-coil galvanometer: deflection is proportional to current, since NIAB balances the spring. Current sensitivity = NAB/k.
- Ammeter conversion: shunt S = I_gG/(I − I_g) in parallel. Voltmeter conversion: R = V/I_g − G in series.
- Cyclotron frequency f = qB/(2πm), independent of speed.
Worked example
A galvanometer of resistance 50 Ω gives full-scale deflection at 1.0 mA. Convert it into a 0–1 A ammeter. The excess current must bypass the coil: I − I_g = 0.999 A. The shunt carries this at the same voltage, so S = I_gG/(I − I_g) = (1.0×10⁻³ × 50)/0.999 = 0.050 Ω, connected in parallel with the galvanometer.
Traps
Dropping sin θ when v is parallel to B; right-hand-rule direction errors; fitting a high resistance as a shunt; using the coil resistance alone in a voltmeter; and measuring θ from the coil plane instead of the normal.