Do not require a medium to propagate.

Carry energy and momentum.

Electromagnetic Spectrum: The full range of electromagnetic waves, ordered by frequency (or wavelength). Includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

Poynting Vector ($\vec{S}$): Represents the direction and rate of energy flow per unit area (power per unit area) of an electromagnetic wave. $$\vec{S} = \frac{1}{\mu_0} (\vec{E} \times \vec{B})$$ The average intensity is $I = \langle S \rangle = \frac{E_{max}B_{max}}{2\mu_0} = \frac{E_{max}^2}{2\mu_0 c} = \frac{c B_{max}^2}{2\mu_0}$.

Radiation Pressure: EM waves exert pressure on surfaces they strike. $$P_{rad} = \frac{I}{c} \quad (\text{for total absorption})$$ $$P_{rad} = \frac{2I}{c} \quad (\text{for total reflection})$$

7. Properties of Materials in EM Fields

Conductors:
- Free charges move easily.
- $\vec{E}=0$ inside a conductor in electrostatic equilibrium.
- Excess charge resides on the surface.
- Potential is constant throughout the conductor.
Dielectrics (Insulators):
- Charges are bound, but can be polarized by an external E-field.
- Reduce the internal E-field by a factor of $\kappa$.
- Permittivity $\epsilon = \kappa \epsilon_0$.
Magnetic Materials:
- Diamagnetism: Weak repulsion from magnetic fields (e.g., water, copper). Induced magnetic moment opposes the applied field.
- Paramagnetism: Weak attraction to magnetic fields (e.g., aluminum, oxygen). Randomly oriented atomic magnetic moments align with the field.
- Ferromagnetism: Strong attraction to magnetic fields (e.g., iron, nickel, cobalt). Domains of aligned atomic moments. Exhibits hysteresis.
Permeability of Material: $\mu = \kappa_m \mu_0$, where $\kappa_m$ is relative permeability.

8. Circuits (DC and AC Fundamentals)

8.1. DC Circuits

Ohm's Law: $V = IR$.
Resistance: $R = \rho L/A$, where $\rho$ is resistivity.
Resistors in Series: $R_{eq} = \sum R_i$.
Resistors in Parallel: $\frac{1}{R_{eq}} = \sum \frac{1}{R_i}$.
Power Dissipated: $P = IV = I^2R = V^2/R$.
Kirchhoff's Rules:
- Junction Rule: Sum of currents entering a junction equals sum of currents leaving ($ \sum I_{in} = \sum I_{out}$). (Conservation of charge)
- Loop Rule: Sum of potential changes around any closed loop is zero ($ \sum \Delta V = 0$). (Conservation of energy)
RC Circuits:
- Charging: $Q(t) = Q_{max}(1 - e^{-t/RC})$, $I(t) = I_{max}e^{-t/RC}$.
- Discharging: $Q(t) = Q_0 e^{-t/RC}$, $I(t) = I_0 e^{-t/RC}$.
- Time Constant: $\tau = RC$.
RL Circuits:
- Current Growth: $I(t) = I_{max}(1 - e^{-t/\tau})$, where $\tau = L/R$.
- Current Decay: $I(t) = I_0 e^{-t/\tau}$.

8.2. AC Circuits (RLC Series Circuit)

Impedance ($Z$): Total opposition to current flow in AC circuits. $V_{rms} = I_{rms}Z$.
Reactance:
- Inductive Reactance: $X_L = \omega L = 2\pi f L$.
- Capacitive Reactance: $X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C}$.