10-Sentence Essentials for MAG-01

The Biot-Savart law dB = (μ_{0}/4π)(I dl sinθ/ $r^{2}$ ) gives the magnetic field of a current element and is the magnetic analogue of Coulomb's law, with μ_{0} = 4π × 10^{-7} T·m/A.
For an infinite straight wire B = μ_{0}I/(2πd), for a circular loop centre B = μ_{0}NI/(2R), for a solenoid B = μ_{0}nI (where n = N/L), and for a toroid B = μ_{0}NI/(2πr) inside the ring.
Ampere's circuital law ∮B·dl = μ_{0}I_enc provides the same results for symmetric configurations and confirms that B is zero outside an ideal solenoid and in the hollow core of a toroid.
The Lorentz force F = qvB sinθ is always perpendicular to the velocity of the charge, which means it does absolutely zero work and changes only the direction of motion, never the speed.
A charge moving perpendicular to B follows a circular path of radius r = mv/(qB), with time period T = 2πm/(qB) — this period is entirely independent of velocity, the most frequently tested fact in NEET.
A current-carrying conductor in field B experiences force F = BIl sinθ; two parallel wires interact with force per unit length F/l = μ_{0} $I_{1}I_{2}$ /(2πd), attracting when currents are in the same direction and repelling when opposite.
A current loop in a magnetic field experiences torque τ = NIAB sinθ = MB sinθ, where the magnetic moment M = NIA has SI unit A· $m^{2}$ ; this principle drives electric motors and the moving coil galvanometer.
A galvanometer is converted to an ammeter by connecting a small shunt S = I_gG/(I − I_g) in parallel, or to a voltmeter by connecting a large resistance R = V/I_g − G in series.
Magnetic materials are classified as diamagnetic (χ < 0, repelled, examples: Cu, Bi), paramagnetic (χ > 0 small, Curie's law χ = C/T, examples: Al, $O_{2}$ ), or ferromagnetic (χ >> 0, domains, hysteresis, examples: Fe, Co, Ni).
Ferromagnets show hysteresis with retentivity (residual B at H = 0) and coercivity (reverse H to demagnetise); soft ferromagnets (low coercivity) are used in transformer cores, while hard ferromagnets (high coercivity) make permanent magnets, and above the Curie temperature all ferromagnets become paramagnetic.