Moving Charges and Magnetism Class 12 Notes (2026-27) — CBSE
Class 12 Physics Chapter 4 notes: Lorentz force, charges in a magnetic field, Biot-Savart and Ampere laws, solenoids, force between wires and torque on a loop.
Moving Charges and Magnetism — Class 12 Physics Notes
Chapter Snapshot
This chapter is about the magnetic effects of moving charges and currents: the force a field exerts on a moving charge (Lorentz force) and on a current-carrying wire, how charges move in a field, and the two tools for finding the field produced by a current — the Biot-Savart law and Ampere's circuital law. It ends with the force between wires, torque on a loop, and the galvanometer.
Board relevance: ~8 marks. Expect a field derivation (Biot-Savart or Ampere) and a force/torque numerical. Directions come from the right-hand rule and F = qv × B.
Syllabus note (rationalised): the cyclotron has been removed. Focus on the Biot-Savart law, Ampere's law, and the galvanometer.
Key Concepts & Definitions
Lorentz force — the total electromagnetic force on a charge q:
F = q(E + v × B)
The magnetic part F = qv × B has magnitude qvB sin θ, is perpendicular to both v and B, and does no work (so it changes direction, not speed).
Motion in a uniform magnetic field (v ⟂ B): the particle moves in a circle.
radius r = mv/qB ; time period T = 2πm/qB ; frequency f = qB/2πm
If v has a component along B, the path is a helix.
Force on a current-carrying conductor:
F = I L × B, magnitude F = BIL sin θ
Formulas — Fields Due to Currents
Biot-Savart law (field of a small current element):
dB = (μ₀/4π)(I dl sin θ)/r² (μ₀ = 4π × 10⁻⁷ T·m/A)
Configuration Magnetic field
Long straight wire (distance a) B = μ₀I/(2πa)
Centre of a circular loop (radius R) B = μ₀I/(2R)
On the axis of a loop (distance x) B = μ₀IR²/[2(R² + x²)^{3/2}]
Inside a long solenoid B = μ₀nI (n = turns per metre)
Toroid B = μ₀nI
Ampere's circuital law: ∮B·dl = μ₀Ienclosed — used for symmetric cases (straight wire, solenoid, toroid).
Force Between Wires, Torque, Galvanometer
Force between two parallel wires (separation d):
F/L = μ₀I₁I₂/(2πd)
Parallel currents attract, antiparallel repel. This defines the ampere (1 A gives 2 × 10⁻⁷ N/m between wires 1 m apart).
Torque on a current loop in a field:
τ = NIAB sin θ = mB sin θ, where m = NIA is the magnetic moment.
Moving-coil galvanometer: a coil in a radial field deflects by φ ∝ I. Current sensitivity = φ/I = NAB/k; converting it to an ammeter needs a low shunt in parallel, to a voltmeter a high resistance in series.
Worked Examples
Example 1 — Circular motion: A proton (m = 1.67 × 10⁻²⁷ kg, q = 1.6 × 10⁻¹⁹ C) moves at 10⁶ m/s perpendicular to a 0.5 T field. Find the radius.
r = mv/qB = (1.67 × 10⁻²⁷)(10⁶)/[(1.6 × 10⁻¹⁹)(0.5)] ≈ 0.021 m (2.1 cm).
Example 2 — Field of a straight wire: Find B at 5 cm from a long wire carrying 10 A.
B = μ₀I/(2πa) = (4π × 10⁻⁷)(10)/(2π × 0.05) = (2 × 10⁻⁷)(10)/0.05 = 4 × 10⁻⁵ T.
Example 3 — Solenoid: A solenoid has 500 turns over 0.5 m carrying 2 A. Find B inside.
n = 500/0.5 = 1000 turns/m. B = μ₀nI = (4π × 10⁻⁷)(1000)(2) ≈ 2.5 × 10⁻³ T.
Example 4 — Torque: A 100-turn coil of area 2 × 10⁻² m² carries 1 A in a 0.5 T field, plane parallel to B. Find the torque.
Plane parallel to B ⇒ θ = 90°. τ = NIAB = 100 × 1 × 2 × 10⁻² × 0.5 = 1 N·m.
Important Question Patterns
1. Lorentz force/motion (2–3 marks): radius r = mv/qB, period T = 2πm/qB; why the magnetic force does no work.
2. Field derivation (3 marks): Biot-Savart for a circular loop, or Ampere's law for a straight wire / solenoid.
3. Force on wire / between wires (2–3 marks): F = BIL sin θ; F/L = μ₀I₁I₂/2πd; attraction vs repulsion.
4. Torque & magnetic moment (3 marks): τ = NIAB sin θ, m = NIA; behaviour of a loop in a field.
5. Galvanometer conversion (3 marks): ammeter (shunt in parallel) and voltmeter (resistance in series); current/voltage sensitivity.
⚡ Quick Revision
- Lorentz force F = q(E + v × B); magnetic part qvB sin θ, ⟂ to v, does no work.
- Circular motion: r = mv/qB, T = 2πm/qB, f = qB/2πm; helix if v has a parallel component.
- Force on wire F = BIL sin θ (F = IL × B).
- Biot-Savart dB = (μ₀/4π)(I dl sin θ)/r². Straight wire B = μ₀I/2πa; loop centre μ₀I/2R; solenoid μ₀nI.
- Ampere's law: ∮B·dl = μ₀Ienc (symmetric cases).
- Parallel wires: F/L = μ₀I₁I₂/2πd (parallel attract, antiparallel repel) → defines the ampere.
- Torque τ = NIAB sin θ = mB sin θ, m = NIA. Galvanometer → ammeter (shunt), voltmeter (series R).
- Removed from syllabus: cyclotron.
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