Physics Lecture: Electromagnetism, Waves, and Optics

Comprehensive vocabulary flashcards covering basic electrostatics, circuitry, magnetism, wave equations, and geometric optics based on the lecture notes.

Coulomb Force ($F$)

The force between two point charges, calculated as $\vec{F} = \frac{1}{4\pi\epsilon_0} \frac{q_1q_2}{r^2} \hat{r}$ and measured in Newtons ($N$).

Electric Field ($\vec{E}$)

The electric field strength describes the force per unit positive test charge ($\vec{E} = \frac{\vec{F}}{q_{Probe}}$), measured in $[N/C]$ or $[V/m]$.

Electric Dipole Moment ($\vec{p}$)

A vector directed from the negative to the positive charge defined as $\vec{p} = Q\vec{l}$, where $\vec{l}$ is the vector between the charge centers.

Electric Flux ($\Phi$)

A measure of the density of electric field lines passing through a surface, given by $\Phi = \int_A \vec{E} \cdot d\vec{A}$ with units of $[Vm]$.

Gauss's Law

States that the total electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space: $\oint_A \vec{E} \cdot d\vec{A} = \frac{Q_{encl}}{\epsilon_0}$.

Charge Densities ($\rho, \sigma, \lambda$)

Volume charge density $\rho = \frac{dq}{dV}$ ($C/m^3$), surface charge density $\sigma = \frac{dq}{dA}$ ($C/m^2$), and line charge density $\lambda = \frac{dq}{dl}$ ($C/m$).

Electric Potential ($\phi$)

Defined as the potential energy per unit charge ($C$); for a point charge relative to infinity, it is $\phi = \frac{1}{4\pi\epsilon_0} \frac{q}{r}$.

Voltage ($U$)

The potential difference between two points, denoting the change in potential energy per Coulomb: $U = \Delta\phi = \phi_b - \phi_a = -\int_a^b \vec{E} \cdot d\vec{s}$.

Electric Flux Density ($D$)

A measure of the free charges generating a field, independent of dielectrics, defined as $\vec{D} = \epsilon_0\vec{E}$ with units of $[C/m^2]$.

Discontinuity ($\Delta E_N$)

The jump in the normal component of the electric field at a charged surface, given by $\Delta E_N = \frac{\sigma}{\epsilon_0}$.

Capacitance ($C$)

A measure of a capacitor's ability to store charge at a given voltage, defined as $C = \frac{Q}{U}$ and measured in Farads ($F$).

Energy Density ($\omega_{el}$)

The energy stored per unit volume in an electric field, given by $\omega_{el} = \frac{1}{2}\epsilon_0 E^2$ (or $\frac{1}{2}\epsilon_r\epsilon_0 E^2$ with a dielectric).

Kirchhoff's Junction Rule (Knotenregel)

Based on charge conservation, the sum of all currents entering and leaving a junction must be zero: $\sum I_{Knoten} = 0$.

Kirchhoff's Loop Rule (Maschenregel)

Based on the conservation of energy, the sum of voltages around a closed loop in a circuit must be zero: $\sum U_{Masche} = 0$.

Ohm's Law

The relationship stating that current is proportional to voltage divided by resistance: $I = \frac{U}{R}$.

Specific Resistance ($\rho$)

A material property that determines resistance based on geometry: $R = \rho \frac{l}{A}$, where $\rho$ is the resistivity.

Lorentz Force ($\vec{F}$)

The magnetic force exerted on a charge $q$ moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$, given by $\vec{F} = q(\vec{v} \times \vec{B})$.

Magnetic Moment ($\vec{\mu}$)

The property of a current loop defined as $\vec{\mu} = N \cdot I \cdot \vec{A}$, where $\vec{A}$ is the surface normal vector.

Ampère's Law

Relates the integrated magnetic field around a closed loop to the electric current passing through the loop: $\oint_C \vec{B} \cdot d\vec{s} = \mu_0 I_c$.

Lenz's Law

States that induced current always creates a magnetic field that opposes the change in the magnetic flux that caused it.

Inductance ($L$)

The property of a conductor where a change in current induces a voltage, defined by $\Phi_{mag} = L \cdot I$ and measured in Henry ($H$).

Reactance ($X_L, X_C$)

The frequency-dependent resistance in AC circuits: inductive reactance is $X_L = \omega L$ and capacitive reactance is $X_C = \frac{1}{\omega C}$.

Impedance ($\tilde{Z}$)

The complex resistance in AC circuits: $\tilde{Z}_R = R$, $\tilde{Z}_L = i\omega L$, and $\tilde{Z}_C = \frac{1}{i\omega C}$.

Poynting Vector ($\vec{S}$)

Represents the direction and magnitude of energy flow in an electromagnetic wave: $\vec{S} = \frac{\vec{E} \times \vec{B}}{\mu_0}$.

Refractive Index ($n$)

A dimensionless number describing how light propagates through a medium: $n = \frac{c}{c_n}$, where $c$ is the speed of light in vacuum.

Brewster's Angle ($\theta_p$)

The angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent surface with no reflection: $\tan(\theta_p) = \frac{n_2}{n_1}$.

Rayleigh Criterion

Defines the limit of resolution for an optical system: $\theta = 1.22 \frac{\lambda}{D}$ for a round opening of diameter $D$.