Chapter 4 — Moving Charges and Magnetism

Chapter 4 of the Class 12 Physics NCERT textbook, "Moving Charges and Magnetism", 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.

• Currents as a source of magnetism — Starting from Oersted's discovery that a current deflects a compass, the chapter establishes the deep link between electricity and magnetism — moving charge is what creates a magnetic field.
• Force on moving charges — The Lorentz force describes how fields push on moving charges without doing work, leading to the circular and helical paths that underpin devices like the cyclotron.
• Calculating magnetic fields — Two complementary tools — the Biot-Savart law for any current element and Ampere's law for symmetric cases — let you find the fields of wires, loops, and solenoids.
• Loops, torque, and measurement — Current loops behave as magnetic dipoles that twist in a field, a principle harnessed by the moving coil galvanometer and its conversion into ammeters and voltmeters.

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.