Magnetism

Concept overview

Magnetism describes the fields produced by moving charges and currents, and the forces those fields exert on other charges and currents. The Biot-Savart law gives the magnetic field due to a current element: dB = (μ₀/4π) (I dl × r̂)/r². The direction is given by the right-hand rule — a critical geometric skill.

Ampere's law is the magnetic analogue of Gauss's law: ∮B·dl = μ₀ I_enc. Applied to symmetric geometries, it directly gives B: infinite straight wire B = μ₀I/(2πr); infinite solenoid B = μ₀nI inside, zero outside; toroid B = μ₀NI/(2πr). Recognising when to use Ampere's law and choosing the right Amperian loop is the workhorse skill.

The force on a moving charge is F = qv × B — always perpendicular to velocity, so no work is done. This forces charged particles to move in circles when B is perpendicular to v, with radius r = mv/(qB) and cyclotron frequency ω = qB/m. Combined electric and magnetic fields give the velocity selector (F_E = F_B when qE = qvB gives v = E/B, selecting a specific speed).

The force on a current-carrying wire is F = IL × B, and two parallel wires attract or repel based on current direction: F/L = μ₀I₁I₂/(2πd). Torque on a current loop in a field is τ = m × B where m = IA is the magnetic moment.

Key formulas & concepts

• Biot-Savart law: dB = (μ₀/4π) I dl × r̂ / r²
• Ampere's law: ∮ B · dl = μ₀ I_enc
• Field near infinite wire: B = μ₀I / (2πr)
• Field inside solenoid: B = μ₀nI (n = turns per unit length)
• Field at centre of loop: B = μ₀I / (2R)
• Force on charge: F = qv × B
• Cyclotron radius: r = mv / (qB); ω = qB/m
• Force between parallel wires: F/L = μ₀ I₁ I₂ / (2πd)

Common mistakes to avoid

• Forgetting that F = qv × B does no work — magnetic force cannot change kinetic energy.
• Applying Ampere's law to a non-symmetric current distribution — same restriction as Gauss's law for electric fields.
• Mixing right-hand rules for current-B versus velocity-force — B curls around current; F is perpendicular to both v and B.
• Using inside-solenoid formula for a short solenoid — B = μ₀nI holds only for infinite (long) solenoid.

JEE Main relevance

JEE Main asks 2 magnetism problems every paper — usually one Biot-Savart or Ampere calculation and one force-on-charge or cyclotron/velocity-selector problem.

JEE Advanced relevance

Advanced problems combine cyclotron motion with drift in crossed fields, or ask about force between non-parallel wires. Torque on a rectangular coil in a uniform field is a standard Advanced pattern.

Previous-year questions (PYQ)

Magnetism PYQs cluster around solenoid/toroid B-field, cyclotron radius, and force between parallel wires. Drill each archetype separately.