PHY332 Electromagnetic Theory I Flashcards

Vocabulary practice flashcards covering basic electromagnetic theory constants, vector calculus operators, charge densities, and fundamental Maxwell's equations based on PHY332 lecture notes.

Coulomb's Law

The mathematical formula for the force between two point charges, given by $F_{12} = \frac{1}{4\pi\epsilon_0} \frac{q_1q_2}{r^2} \hat{r}_{12}$, where charges are denoted by $q_1$ and $q_2$.

Permittivity of Free Space ($\epsilon_0$)

A physical constant with a value of approximately $8.8542 \times 10^{-12}\,C^2 N^{-1} m^{-2}$, used in the calculation of electric fields and potentials.

Electric Field ($E$)

Defined as the limit of the force divided by a test charge as the test charge approaches zero, expressed as $E = \lim_{q_t \to 0} \frac{F}{q_t}$.

Linear Charge Density ($\lambda$)

The measure of electric charge per unit length, defined as $\lambda = \lim_{\Delta \ell \to 0} \frac{\Delta q}{\Delta \ell}$.

Surface Charge Density ($\sigma$)

The measure of electric charge per unit area, defined as $\sigma = \lim_{\Delta S \to 0} \frac{\Delta q}{\Delta S}$.

Volume Charge Density ($\rho$)

The measure of electric charge per unit volume, defined as $\rho = \lim_{\Delta V \to 0} \frac{\Delta q}{\Delta V}$.

Gradient ($\nabla f$)

A vector differential operator that, in Cartesian coordinates, is defined as $\nabla f = \hat{i} \frac{\partial f}{\partial x} + \hat{j} \frac{\partial f}{\partial y} + \hat{k} \frac{\partial f}{\partial z}$.

Divergence ($\nabla \cdot F$)

A measure of a vector field's outward flux from an infinitesimal volume, given by $\nabla \cdot F = \frac{\partial F_x}{\partial x} + \frac{\partial F_y}{\partial y} + \frac{\partial F_z}{\partial z}$.

Curl ($\nabla \times F$)

A vector operator that indicates the infinitesimal rotation of a vector field, computed using the determinant of a matrix containing unit vectors, partial derivatives, and vector components.

Laplacian Operator ($\nabla^2$)

The divergence of the gradient, mathematically represented as $\nabla^2 = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2}$.

Poisson's Equation

A differential equation for the scalar potential $\phi$ in the presence of a charge density $\rho$, expressed as $\nabla^2 \phi = -\frac{\rho}{\epsilon_0}$.

Laplace's Equation

A partial differential equation for the scalar potential $\phi$ in regions where the charge density is zero, expressed as $\nabla^2 \phi = 0$.

Divergence Theorem

Relates the volume integral of the divergence of a vector field to the surface integral of that field over the boundary: $\int \int \int_V (\nabla \cdot F) dV = \oint_S (F \cdot \hat{n}) dS$.

Stokes' Theorem

Relates the surface integral of the curl of a vector field to the line integral of that field over the boundary curve: $\oint_c F \cdot d\vec{\ell} = \int \int_S (\nabla \times F) \cdot d\vec{S}$.

Faraday's Law (Differential Form)

One of Maxwell's equations stating that a time-varying magnetic field creates an electric field, given by $\nabla \times E = -\frac{\partial B}{\partial t}$.

Ampere's Law (Modified)

Relates the curl of the magnetic field intensity to the current density and displacement current density: $\nabla \times H = J + \frac{\partial D}{\partial t}$.

Gauss's Law for Magnetism

States that the divergence of the magnetic field is zero, represented as $\nabla \cdot B = 0$.

Poynting Vector ($S$)

Represents the directional energy flux of an electromagnetic field, defined by the cross product $S = E \times H$.

Intrinsic Impedance ($\eta$)

The ratio of the magnitudes of the electric field to the magnetic field in a medium, defined as $\eta = \sqrt{\frac{\mu}{\epsilon}}$, where in free space $\eta \approx 377\,\Omega$.

Speed of Light ($c$)

The propagation speed of electromagnetic waves in a vacuum, calculated as $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$ which is approximately $3 \times 10^8\,m/s$.