Chapter 4 — Moving Charges and Magnetism

Chapter 4 of Class 12 Physics Part I covers Moving Charges and Magnetism, explaining how electric currents and moving charges produce magnetic fields and how magnetic fields exert forces on moving charges and current-carrying conductors, governed by laws including the Lorentz force, Biot-Savart law, and Ampere's Circuital Law.

Class 12 Physics Chapter 4 — Moving Charges and Magnetism — begins with Oersted's 1820 discovery that a current-carrying wire deflects a compass needle. It derives the Lorentz force F = q(v × B + E) on a moving charge, explores circular and helical motion of charged particles in magnetic fields, and introduces the cyclotron frequency ν = qB/2πm. The Biot-Savart law gives the field due to a current element, while Ampere's Circuital Law (∮B·dl = μ₀I) is used to find fields of long wires and solenoids (B = μ₀nI). The chapter also covers torque on current loops, the magnetic dipole moment m = NIA, and the moving coil galvanometer — including its conversion to an ammeter (shunt resistor in parallel) or voltmeter (large resistor in series).

1. 01The Lorentz force on a charge q moving with velocity v in magnetic field B is F = q(v × B), always perpendicular to v, so the magnetic force does no work on the particle.
2. 02A charged particle moving perpendicular to a uniform magnetic field follows a circular path of radius r = mv/qB; the cyclotron frequency ν = qB/2πm is independent of the particle's speed.
3. 03The Biot-Savart law states dB = (μ₀/4π)(I dl × r̂)/r², giving the magnetic field contribution from an infinitesimal current element; the field at the centre of a circular loop of radius R is B = μ₀I/2R.
4. 04Ampere's Circuital Law (∮B·dl = μ₀I) gives the field outside a long straight wire as B = μ₀I/2πR and inside a long solenoid as B = μ₀nI, where n is turns per unit length.
5. 05Parallel currents attract each other and anti-parallel currents repel; this interaction defines the SI unit of current — the ampere.
6. 06A current loop in a uniform magnetic field experiences a torque τ = m × B (where m = NIA is the magnetic moment) but no net force; the moving coil galvanometer exploits this torque, balanced by a restoring spring, to measure current.