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 [M$LT^{-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.
Part of MAG-01 — Magnetic Effects of Current & Magnetism
Complete Topic Guide — Magnetic Effects of Current & Magnetism
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