Section 1: Biot-Savart Law and Field Configurations

The Biot-Savart law quantifies the magnetic field contribution dB from an infinitesimal current element. Its form — dB proportional to I dl sinθ / $r^{2}$ — is the direct magnetic analogue of Coulomb's law for electric fields. Integration over different geometries gives the field for practical configurations. For an infinite wire, B = μ_{0}I/(2πd) drops with 1/d (inverse first power, not inverse square, because the wire is an extended source). For a circular loop's centre, B = μ_{0}NI/(2R) increases with more turns N and more current I, but decreases with larger radius R. The axial formula B = μ_{0}N$IR^{2}$/[2($R^{2}$+$x^{2}$)^(3/2)] reduces to the centre formula at x = 0 and falls off rapidly with distance, eventually going as 1/$x^{3}$ for x >> R (dipole behaviour).

Section 2: Ampere's Circuital Law

Ampere's law ∮B·dl = μ_{0}I_enc is the integral version of Biot-Savart, offering computational efficiency when symmetry is high. The solenoid result B = μ_{0}nI inside (zero outside) relies on this symmetry: field is uniform and axial inside, negligible outside. The toroid confines the field to its ring cross-section (B = μ_{0}NI/2πr), with no field in the hollow core or exterior — a stark contrast with the solenoid. Both are essential NEET configurations.

Section 3: Lorentz Force and Motion of Charged Particles

The force F = qvB sinθ is always perpendicular to velocity — it is a deflecting, not accelerating, force. Circular motion results when v ⊥ B; the radius r = mv/(qB) depends on momentum mv and the product qB. The cyclotron frequency f = qB/(2πm) is the basis of the cyclotron particle accelerator. The velocity-independence of T is arguably the single most important testable fact in this section. Helical motion (when v has components both along and perpendicular to B) has pitch p = v_∥ × T.

Section 4: Forces on Conductors and Torque

The force F = BIl sinθ on a straight conductor follows from integrating the Lorentz force over charge carriers in the conductor. The force per unit length between parallel wires F/l = μ_{0}$I_{1}I_{2}$/(2πd) is both a practical result and the definition of the ampere. The torque τ = NIAB sinθ on a current loop is the mechanism behind electric motors and the galvanometer. Maximum torque occurs at θ = 90° (plane of loop parallel to B); zero torque at θ = 0° or 180° (stable/unstable equilibrium).

Section 5: Moving Coil Galvanometer and Conversions

The galvanometer measures current via the torque balance NIAB = kθ. Its sensitivity θ/I = NAB/k can be increased by maximising N, A, B or minimising spring constant k. Practical use requires conversion: an ammeter shunts most current around the galvanometer (S ≈ I_gG/(I − I_g), very small), while a voltmeter adds a large series resistance (R = V/I_g − G ≈ V/I_g for small I_g) to sample only a tiny current proportional to voltage.

Section 6: Magnetic Materials and Hysteresis

The three-way classification — diamagnetic, paramagnetic, ferromagnetic — is based on atomic structure and exchange interactions. The relation B = μ_{0}μ_rH = μ_{0}(H + M) connects the macroscopic fields B (total flux density), H (applied field), and M (magnetisation). The hysteresis loop encodes both the material's memory (retentivity) and resistance to demagnetisation (coercivity). Energy dissipated per cycle = area of loop, making loop area a critical factor in transformer core material selection.