| Cue Column | Notes Column |
|---|---|
| What is Biot-Savart law? | dB = (μ_{0}/4π)(I dl sinθ / ); magnetic analog of Coulomb's law; direction by right-hand rule (dl × r̂) |
| B for infinite straight wire | B = μ_{0}I/(2πd); concentric circles; right-hand thumb rule |
| B at center of circular loop | B = μ_{0}NI/(2R); on axis: B = μ_{0}N/[2(+)^(3/2)] |
| B inside solenoid | B = μ_{0}nI (uniform, where n = N/L); outside ≈ 0 |
| Ampere's circuital law | ∮B·dl = μ_{0}I_enc; valid for any closed loop; useful for high-symmetry cases |
| Toroid field | B = μ_{0}NI/(2πr) inside; zero outside |
| Lorentz force | F = q(E + v×B); magnetic part always ⊥ to v → does NO work |
| Circular motion in B | r = mv/(qB); T = 2πm/(qB) — independent of velocity |
| Helical motion | If v has component along B: path is helix; pitch = v_∥ × T |
| Force on conductor | F = BIl sinθ; direction by F = Il × B |
| Force between parallel wires | F/l = μ_{0}/(2πd); same direction → attract; opposite → repel |
| Torque on current loop | τ = NIAB sinθ = MB sinθ; M = NIA (magnetic moment) |
| Galvanometer → Ammeter | Shunt S = I_gG/(I − I_g) in parallel; very low resistance |
| Galvanometer → Voltmeter | Series R = V/I_g − G; very high resistance |
| Magnetic materials | Dia (χ < 0, repelled); Para (χ > 0 small); Ferro (χ >> 0, retains magnetism) |
| Curie's law | χ = C/T for paramagnets; above Curie temp, ferromagnets → paramagnetic |
| Hysteresis loop | Retentivity = residual B after H=0; Coercivity = reverse H to demagnetize |
| Soft vs hard ferromagnets | Soft: low coercivity → electromagnets; Hard: high coercivity → permanent magnets |
Summary: The chapter connects the origin of magnetic fields (Biot-Savart, Ampere) to the forces they exert (Lorentz, torque on loops) and concludes with material response (dia/para/ferromagnetism). The key NEET traps are: (1) magnetic force does no work, (2) time period T = 2πm/qB is velocity-independent, (3) for ammeter use shunt (parallel), for voltmeter use series resistance. Dimensional formula for B is [MT^{-2}$$A^{-1}]; for magnetic moment M is [].