Magnetic Effects of Current and Magnetism
This domain joins moving charges to magnetic fields: Biot–Savart law, Ampere's circuital law, force on conductors, the cyclotron, the moving-coil galvanometer and the magnetic properties of matter.
Core rules
- Biot–Savart: dB = (μ₀/4π)(I dl × r̂)/r². A long straight wire gives B = μ₀I/2πr; the centre of a circular loop gives B = μ₀I/2R; well inside a solenoid B = μ₀nI.
- Ampere's circuital law: ∮B·dl = μ₀I(enclosed).
- Force on a conductor F = BIl sinθ; on a moving charge F = qvB sinθ, always perpendicular to v, so magnetic force does no work.
- Parallel currents attract when in the same direction, repel when opposite; F/l = μ₀I₁I₂/2πd.
- Cyclotron frequency f = qB/2πm, independent of speed.
- A galvanometer becomes an ammeter with a small shunt in parallel and a voltmeter with a high resistance in series.
- Dia-, para- and ferromagnetic materials have small negative, small positive and large positive susceptibility; ferromagnets show hysteresis and retentivity.
Worked example
Two long parallel wires 0.10 m apart carry 5 A each in the same direction. F/l = (μ₀/2π)(I₁I₂/d) = (2×10⁻⁷)(25/0.10) = 5×10⁻⁵ N m⁻¹. The force is attractive because the currents are parallel.
Traps
Reversing the order in dl × r̂; using μ₀nI outside the solenoid; claiming magnetic force changes speed; putting the shunt in series with a galvanometer.