Magnetic Effects of Current and Magnetism
Magnetic Effects of Current and Magnetism covers fields produced by currents, forces on moving charges and wires, torque on loops, galvanometers and magnetic materials. The exam often asks direction plus magnitude.
Core rules
- Biot–Savart: dB = (μ₀/4π)(I dl sinθ/r²). Straight wire B = μ₀I/(2πr); centre of a circular loop B = μ₀I/(2R).
- Ampere's law relates the line integral of B around a loop to enclosed current. A long solenoid has B = μ₀nI near its centre.
- Magnetic force on a charge F = qvB sinθ, always perpendicular to v and B, so it does no work. On a straight wire F = BIL sinθ.
- A current loop has magnetic moment m = NIA; torque τ = mB sinθ. A moving-coil galvanometer uses a radial field and a spring to give a linear deflection.
- Diamagnetic materials are weakly repelled; paramagnetic weakly attracted; ferromagnetic strongly attracted and can retain magnetism.
Worked example
A proton (q = 1.6×10⁻¹⁹ C) moves at 2.0×10⁶ m/s perpendicular to a 0.50 T field. F = qvB = (1.6×10⁻¹⁹)(2.0×10⁶)(0.50) = 1.6×10⁻¹³ N. Direction follows the right-hand rule for a positive charge: v×B, then adjusted by q.
Traps
Using sinθ = 1 when the velocity is parallel to B (then force is zero); confusing magnetic field direction with force direction; and thinking a magnetic force changes a charged particle's speed rather than only its direction.