Core NEET Facts for MAG-01

Biot-Savart law: dB = (μ_{0}/4π)(I dl sinθ / $r^{2}$ ); direction by right-hand rule (dl × r̂); magnetic analogue of Coulomb's law
μ_{0} = 4π × 10^{-7} T·m/A; dimensional formula [M $LT^{-2}$$A^{-2}$ ]; B has [ $MT^{-2}$$A^{-1}$ ]
Infinite straight wire: B = μ_{0}I/(2πd); concentric circles; right-hand thumb rule for direction
Circular loop centre: B = μ_{0}NI/(2R); increases with N and I, decreases with R
Circular loop axis: B = μ_{0}N $IR^{2}$ /[2( $R^{2}$ + $x^{2}$ )^(3/2)]; at x=R: B = B_centre/(2√2)
Solenoid: B = μ_{0}nI inside (uniform); n = N/L; B ≈ 0 outside; depends on n not N
Toroid: B = μ_{0}NI/(2πr) inside ring; B = 0 in hollow core AND outside
Ampere's law: ∮B·dl = μ_{0}I_enc; use only with high symmetry
Lorentz force: F = qvB sinθ; ALWAYS perpendicular to v; does ZERO work; changes direction not speed
Circular path: r = mv/(qB); [L] = m; radius depends on velocity
Time period: T = 2πm/(qB); [T] = s; DOES NOT depend on velocity (most tested NEET fact)
Cyclotron frequency: f = qB/(2πm); velocity-independent
Helical path: when v has both parallel and perpendicular components to B; pitch = v_∥ × T
Force on conductor: F = BIl sinθ; direction: F = Il × B
Parallel wires: F/l = μ_{0} $I_{1}I_{2}$ /(2πd); same direction → attract; opposite → repel
Definition of 1 A: current producing $2 \times 10^{-7}$ N/m between two infinite wires 1 m apart
Torque on loop: τ = NIAB sinθ = MB sinθ; magnetic moment M = NIA; [ $AL^{2}$ ]
Galvanometer → Ammeter: shunt S = I_gG/(I − I_g) in PARALLEL; R_eff very low
Galvanometer → Voltmeter: series R = V/I_g − G; R_eff very high
Diamagnetic: χ < 0; μᵣ < 1; repelled; Cu, Bi, $H_{2}O$ ; temperature-independent
Paramagnetic: χ > 0 small; μᵣ slightly > 1; weakly attracted; Al, $O_{2}$ ; Curie law χ = C/T
Ferromagnetic: χ >> 0; μᵣ >> 1 (up to 10^{5}); Fe, Co, Ni; domains; hysteresis
Retentivity: residual B at H = 0 (y-intercept of hysteresis loop)
Coercivity: reverse H to bring B to 0 (x-intercept of hysteresis loop)
Curie temperature: Fe = 770°C; Co = 1115°C; Ni = 358°C; above this → paramagnetic