Magnetic effects of current is one of the most consistently tested chapters in NEET Physics, contributing 2–3 questions per year. The chapter is built on two foundational laws — Biot-Savart and Ampere — that describe how currents generate magnetic fields, followed by the Lorentz force law that describes how magnetic fields act on charges and conductors, and concluding with magnetic materials.

Origin of Magnetic Fields

The Biot-Savart law is the starting point: a current element I dl produces a magnetic field dB = (μ_{0}/4π)(I dl sinθ / $r^{2}$) at distance r, where θ is the angle between the current element direction and the position vector. The permeability of free space μ_{0} = 4π × 10^{-7} T·m/A has dimensional formula [MLT^{-2}$$A^{-2}]. The SI unit of B is the tesla (T), with dimensional formula [MT^{-2}$$A^{-1}].

For an infinite straight wire, this integrates to B = μ_{0}I/(2πd), where d is perpendicular distance. The field forms concentric circles — direction given by the right-hand thumb rule. For a finite wire subtending angles α and β, B = (μ_{0}I/4πd)(sinα + sinβ). At the centre of a circular coil of N turns and radius R, B = μ_{0}NI/(2R). At an axial point distance x from the centre, B = μ_{0}N$IR^{2}$/[2($R^{2}$+$x^{2}$)^(3/2)].

Ampere's circuital law ∮B·dl = μ_{0}I_enc provides a more powerful approach for symmetric configurations. For an ideal solenoid (n turns per unit length), the field inside is B = μ_{0}nI — perfectly uniform — and essentially zero outside. Note that n = N/L; the field depends on turns per unit length, not total turns. For a toroid, B = μ_{0}NI/(2πr) inside the ring and zero both in the hollow centre and outside.

Forces on Charges and Conductors

The Lorentz force on a charge q moving with velocity v in combined electric and magnetic fields is F = q(E + v×B). The magnetic component F = qvB sinθ is always perpendicular to the velocity. This perpendicularity has a profound consequence: magnetic force does NO work on a moving charge (work = F·ds = 0 since F ⊥ ds). The charge's speed — and hence kinetic energy — is unchanged; only direction changes.

When v is perpendicular to B, the Lorentz force provides the centripetal force: qvB = $mv^{2}$/r, giving radius r = mv/(qB). The time period T = 2πm/(qB) and frequency f = qB/(2πm) are both independent of velocity — the key NEET insight. A faster particle traces a larger circle in exactly the same time. If velocity has a component v_∥ along B, the particle follows a helix with pitch p = v_∥ × T.

The force on a current-carrying conductor of length l in field B is F = BIl sinθ, directed by F = Il × B. For two parallel wires carrying currents $I_{1}$ and $I_{2}$ separated by distance d, the force per unit length is F/l = μ_{0}I_{1}$$I_{2}/(2πd). Wires with currents in the same direction attract; opposite directions repel. This relationship defines the SI base unit of current: 1 ampere is the current that produces a force of $2 \times 10^{-7}$ N/m between two infinite parallel wires 1 m apart.

A current loop in a magnetic field experiences a torque τ = NIAB sinθ, where M = NIA is the magnetic moment ([M] = [$AL^{2}$], SI unit: A·$m^{2}$). This is the operating principle of the moving coil galvanometer: the magnetic torque NIAB is balanced by the restoring spring torque kθ, giving deflection θ = (NAB/k)I. To convert to an ammeter, a shunt resistance S = I_gG/(I − I_g) is connected in parallel (very low resistance). To convert to a voltmeter, a series resistance R = V/I_g − G is connected (very high resistance).

Magnetic Materials

All materials respond to external magnetic fields; the difference lies in degree and sign. Diamagnetic materials (Cu, Bi, $H_{2}O$) have susceptibility χ < 0 and relative permeability μᵣ < 1. They are weakly repelled by external fields and move toward weaker field regions. Their response is temperature-independent.

Paramagnetic materials (Al, $O_{2}$, Na) have small positive χ and μᵣ slightly greater than 1. They are weakly attracted by external fields. Their susceptibility obeys Curie's law: χ = C/T, decreasing with rising temperature. Ferromagnetic materials (Fe, Co, Ni) have χ >> 1 and μᵣ up to 10^{5}. They possess permanent magnetic domains — regions of aligned atomic magnetic moments. In an external field, domain walls shift and aligned domains grow, producing strong magnetisation.

Ferromagnets exhibit hysteresis: the B–H curve traces a loop rather than a single path. When H returns to zero, a residual field B_r (retentivity) remains. A reverse field −H_c (coercivity) is needed to reduce B to zero. Soft ferromagnets (soft iron) have low coercivity and small hysteresis loop area — ideal for transformer cores and electromagnets where rapid switching is needed. Hard ferromagnets (steel, Alnico) have high coercivity and retentivity — ideal for permanent magnets and magnetic storage.

Above the Curie temperature (770°C for Fe, 1115°C for Co, 358°C for Ni), ferromagnets lose their domain structure and become paramagnetic. The connection μᵣ = 1 + χ links permeability and susceptibility across all material types.