Biot-Savart Law: $d\vec{B} = \frac{\mu_0}{4\pi} \frac{I d\vec{l} \times \hat{r}}{r^2}$
Magnetic field:
- Straight wire: $B = \frac{\mu_0 I}{2\pi r}$
- Circular loop (center): $B = \frac{\mu_0 I}{2R}$
- Solenoid: $B = \mu_0 n I$
- Toroid: $B = \frac{\mu_0 N I}{2\pi r}$
Ampere's Circuital Law: $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}$
Lorentz Force: $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$
Magnetic Force on a current-carrying wire: $\vec{F} = I(\vec{l} \times \vec{B})$
Magnetic moment of current loop: $\vec{M} = I\vec{A}$
Torque on current loop: $\vec{\tau} = \vec{M} \times \vec{B}$
Moving Coil Galvanometer: $I = k\theta$

Magnetic Flux: $\Phi_B = \int \vec{B} \cdot d\vec{A}$
Faraday's Law: $\mathcal{E} = -\frac{d\Phi_B}{dt}$
Motional EMF: $\mathcal{E} = (Blv)$ (if $\vec{B}, \vec{l}, \vec{v}$ are mutually perpendicular)
Self-Inductance: $\Phi_B = LI$, $\mathcal{E} = -L\frac{dI}{dt}$
Mutual Inductance: $\Phi_{B2} = M I_1$, $\mathcal{E}_2 = -M\frac{dI_1}{dt}$
Energy Stored in Inductor: $U = \frac{1}{2}LI^2$
Energy Density in B-field: $u_B = \frac{B^2}{2\mu_0}$

Instantaneous Voltage/Current: $V = V_0 \sin(\omega t)$, $I = I_0 \sin(\omega t + \phi)$
RMS Values: $V_{rms} = \frac{V_0}{\sqrt{2}}$, $I_{rms} = \frac{I_0}{\sqrt{2}}$
Reactance:
- Inductive Reactance: $X_L = \omega L$
- Capacitive Reactance: $X_C = \frac{1}{\omega C}$
Impedance: $Z = \sqrt{R^2 + (X_L - X_C)^2}$
Phase Angle: $\tan\phi = \frac{X_L - X_C}{R}$
Power in AC Circuit: $P_{avg} = V_{rms}I_{rms}\cos\phi$ (Power Factor: $\cos\phi = \frac{R}{Z}$)
Resonance (Series RLC): $X_L = X_C \Rightarrow \omega_0 = \frac{1}{\sqrt{LC}}$
Quality Factor: $Q = \frac{\omega_0 L}{R} = \frac{1}{R}\sqrt{\frac{L}{C}}$
Transformer: $\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s}$ (ideal)

Speed of EM waves in vacuum: $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} = 3 \times 10^8 \text{ m/s}$
Speed in medium: $v = \frac{1}{\sqrt{\mu \epsilon}}$
Relation between E and B fields: $E = cB$
Energy Density: $u = u_E + u_B = \frac{1}{2}\epsilon_0 E^2 + \frac{B^2}{2\mu_0} = \epsilon_0 E^2 = \frac{B^2}{\mu_0}$
Poynting Vector: $\vec{S} = \frac{1}{\mu_0}(\vec{E} \times \vec{B})$ (Energy flow per unit area per unit time)
Momentum carried by EM wave: $p = \frac{U}{c}$
EM Spectrum: Radio, Microwave, IR, Visible, UV, X-ray, Gamma ray (increasing freq/energy, decreasing wavelength)

Reflection: $\angle i = \angle r$
Mirror Formula: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ (concave $f<0$, convex $f>0$)
Magnification: $m = -\frac{v}{u} = \frac{h_i}{h_o}$
Refraction: Snell's Law: $n_1 \sin\theta_1 = n_2 \sin\theta_2$