Magnetic Effects of Current and Magnetism
What this domain tests
This domain covers the Biot–Savart and Ampère results, force on moving charges and on current-carrying wires, torque on a current loop, the moving-coil galvanometer, and the magnetic properties of matter.
Core rules
- Long straight wire B = μ₀I/2πr; centre of a coil B = μ₀NI/2R; solenoid B = μ₀nI, where n is turns per metre and μ₀ = 4π×10⁻⁷ T m A⁻¹.
- F = qvB sinθ, perpendicular to v, so magnetic force does no work. A charge moving perpendicular to B follows a circle of radius r = mv/qB; the period 2πm/qB is independent of speed.
- F = BIL sinθ on a wire; parallel currents attract, antiparallel currents repel.
- τ = NIAB sinθ on a loop; a galvanometer becomes an ammeter with a low shunt in parallel and a voltmeter with a high resistance in series.
Worked example
A proton (m = 1.67×10⁻²⁷ kg, q = 1.6×10⁻¹⁹ C) moves at 2×10⁶ m/s perpendicular to a 0.5 T field. Find the force and the radius. F = qvB = (1.6×10⁻¹⁹)(2×10⁶)(0.5) = 1.6×10⁻¹³ N. r = mv/qB = (1.67×10⁻²⁷)(2×10⁶)/[(1.6×10⁻¹⁹)(0.5)] = 3.34×10⁻²¹/8.0×10⁻²⁰ ≈ 4.2×10⁻² m, about 4 cm. Since v ⊥ B, sinθ = 1 throughout.
Traps that cost marks
- Using sinθ when the charge travels along the field - the force is then zero.
- Believing the magnetic force changes speed; it only bends the path.
- Connecting a shunt in series with a galvanometer instead of in parallel.
- Mixing n (turns per metre) with N (total turns).
- Ignoring the direction rules: Fleming's left hand for force, right-hand grip for the field of a wire.