Constant: $\mu_0 = 4\pi \times 10^{-7}\ \text{T·m/A}$; $[\mu_0] = [MLT^{-2}A^{-2}]$

Biot-Savart: $dB = \frac{\mu_0}{4\pi}\frac{I\,dl\sin\theta}{r^2}$; $[B] = [MT^{-2}A^{-1}]$

Field Configurations: $B_{\text{wire}} = \frac{\mu_0 I}{2\pi d},\quad B_{\text{loop,centre}} = \frac{\mu_0 NI}{2R},\quad B_{\text{axis}} = \frac{\mu_0 NIR^2}{2(R^2+x^2)^{3/2}}$ $B_{\text{solenoid}} = \mu_0 nI\ (n=N/L),\quad B_{\text{toroid}} = \frac{\mu_0 NI}{2\pi r}$

Ampere's Law: $\oint \vec{B}\cdot d\vec{l} = \mu_0 I_{\text{enc}}$

Lorentz Force: $F = qvB\sin\theta$; $[F]=[MLT^{-2}]$; perpendicular to v → zero work

Circular Motion: $r = \frac{mv}{qB}\ [L],\quad T = \frac{2\pi m}{qB}\ [T],\quad f = \frac{qB}{2\pi m}\ [T^{-1}]$

Conductor Force: $F = BIl\sin\theta\ [MLT^{-2}]$

Parallel Wires: $\frac{F}{l} = \frac{\mu_0 I_1 I_2}{2\pi d}\ [MT^{-2}]$; N/m

Torque and Magnetic Moment: $\tau = NIAB\sin\theta = MB\sin\theta\ [ML^2T^{-2}];\ M = NIA\ [AL^2]$

Galvanometer Conversions: $S = \frac{I_g G}{I - I_g}\ [\Omega],\quad R = \frac{V}{I_g} - G\ [\Omega]$

Curie's Law: $\chi = C/T$ (paramagnets); $\mu_r = 1 + \chi$ (all materials)

Key values: $e = 1.6\times10^{-19}$ C; $m_p = 1.67\times10^{-27}$ kg; $m_e = 9.1\times10^{-31}$ kg