Magnetic Effects of Electric Current and Magnetism
This domain covers Biot-Savart law, fields of a straight wire, a circular loop and a solenoid, Ampere's law, force on a current-carrying conductor, the moving-coil galvanometer, and the magnetic properties of materials.
Core rules
- Biot-Savart: dB = (μ₀/4π)(I dl sinθ)/r².
- Long straight wire B = μ₀I/2πa. Centre of a circular coil B = μ₀NI/2r. Solenoid B = μ₀nI inside, near zero outside.
- Ampere's circuital law: ∮B·dl = μ₀I(enclosed).
- Force on a conductor F = BIL sinθ; between parallel wires F/L = μ₀I₁I₂/2πd, attractive for like-direction currents.
- Torque on a loop τ = NIAB sinθ. Moving-coil galvanometer: τ = NIAB = kφ, giving I ∝ φ.
- Ammeter: low resistance shunt in parallel. Voltmeter: high resistance in series. Conversion factors use S = I(g)G/(I − I(g)).
- Magnetic dipole moment m = NIA; torque mB sinθ, energy −mB cosθ.
- Materials: diamagnetic (χ small negative), paramagnetic (small positive, Curie law), ferromagnetic (large, hysteresis with retentivity and coercivity).
Worked example
A coil of 100 turns and radius 0.10 m carries 0.5 A. At the centre, B = μ₀NI/2r = (4π×10⁻⁷ × 100 × 0.5)/(2 × 0.10) = 6.28×10⁻⁵/0.20 = 3.14×10⁻⁴ T, about the strength of the Earth's field times a few.
Traps
- Using the on-axis formula at the centre of a loop, or mixing radius with diameter.
- Reversing the current direction rule when finding field direction.
- Connecting a shunt across a galvanometer to make a voltmeter; a shunt makes an ammeter.