Moving Charges and Magnetism
What is examined
Moving Charges and Magnetism tests the Biot–Savart law, field of a loop and solenoid, force on moving charges and current-carrying conductors, circular motion in a magnetic field, torque on a loop and the moving-coil galvanometer.
Core rules
- Biot–Savart: dB = (μ₀/4π)I dl sin θ/r²; μ₀/4π = 10⁻⁷ T m A⁻¹.
- Centre of a circular loop: B = μ₀I/2R. On the axis: B = μ₀IR²/[2(R²+x²)^{3/2}].
- Long solenoid: B = μ₀nI inside, about zero outside. Ampere's circuital law: ∮B·dl = μ₀I_enclosed.
- Force F = qvB sin θ; F = BIL sin θ on a wire. Direction by right-hand rule or Fleming's left-hand rule.
- Circular path radius r = mv/(qB), period T = 2πm/(qB), independent of speed; cyclotron frequency f = qB/(2πm).
- Torque on a coil: τ = NIAB sin θ. Moving-coil galvanometer: NIAB balances kφ, so I ∝ φ.
- Ammeter: low-resistance shunt in parallel, S = I_g G/(I − I_g). Voltmeter: high resistance in series, R = V/I_g − G.
Worked example
An electron (m = 9.1×10⁻³¹ kg) moves at 3.0×10⁶ m s⁻¹ perpendicular to B = 0.50 T. Find r. r = mv/(qB) = (9.1×10⁻³¹ × 3.0×10⁶)/(1.6×10⁻¹⁹ × 0.50) = 2.73×10⁻²⁴/8.0×10⁻²⁰ ≈ 3.4×10⁻⁵ m. Reasoning: perpendicular motion gives maximum force and a circle; the speed does not change because F is always perpendicular to v.
Traps
Using the angle between v and the plane instead of between v and B; forgetting sin θ; writing r = qB/(mv); and thinking a voltmeter is made by adding a shunt.