Magnetic Effects of Current & Magnetism
├── SOURCES OF MAGNETIC FIELD
│   ├── Biot-Savart Law
│   │   ├── dB = (μ_{0}/4π)(I dl sinθ / $r^{2}$)
│   │   ├── Infinite wire: B = μ_{0}I/(2πd)
│   │   ├── Circular loop centre: B = μ_{0}NI/(2R)
│   │   └── Circular loop axis: B = μ_{0}N$IR^{2}$/[2($R^{2}$+$x^{2}$)^(3/2)]
│   └── Ampere's Circuital Law
│       ├── ∮B·dl = μ_{0}I_enc
│       ├── Solenoid: B = μ_{0}nI (inside)
│       └── Toroid: B = μ_{0}NI/(2πr) inside ring
│
├── FORCES DUE TO MAGNETIC FIELD
│   ├── On Moving Charges (Lorentz Force)
│   │   ├── F = qvB sinθ (⊥ to v → no work)
│   │   ├── Circular path: r = mv/(qB)
│   │   ├── Time period: T = 2πm/(qB) [velocity-independent]
│   │   └── Helical path if v has component along B
│   └── On Current-Carrying Conductors
│       ├── Force on wire: F = BIl sinθ
│       ├── Parallel wires: F/l = μ_{0}$I_{1}I_{2}$/(2πd)
│       │   ├── Same direction → Attract
│       │   └── Opposite direction → Repel
│       └── Torque on loop: τ = NIAB sinθ = MB sinθ
│           └── Magnetic moment: M = NIA [$AL^{2}$]
│
├── INSTRUMENTS
│   └── Moving Coil Galvanometer
│       ├── Principle: τ = NIAB (magnetic) = kθ (spring)
│       ├── Deflection θ = (NAB/k)I
│       ├── → Ammeter: shunt S = I_gG/(I−I_g) [parallel]
│       └── → Voltmeter: series R = V/I_g − G [series]
│
└── MAGNETIC MATERIALS
    ├── Diamagnetic
    │   ├── χ < 0, μᵣ < 1
    │   ├── Examples: Cu, Bi, $H_{2}O$
    │   └── Repelled; temperature-independent
    ├── Paramagnetic
    │   ├── 0 < χ << 1, μᵣ slightly > 1
    │   ├── Examples: Al, $O_{2}$, Pt
    │   └── Weakly attracted; Curie's law: χ = C/T
    └── Ferromagnetic
        ├── χ >> 0, μᵣ >> 1
        ├── Examples: Fe, Co, Ni
        ├── Domains, hysteresis loop
        ├── Retentivity (y-intercept of loop)
        ├── Coercivity (x-intercept of loop)
        ├── Above Curie temp → paramagnetic
        ├── Soft iron: low coercivity → transformer cores
        └── Hard iron/steel: high coercivity → permanent magnets