Electromagnetism

Flashcards from notes on Electromagnetism; University of Oxford, Second Year, Part A2 Michaelmas Term 2018

Scalar Potential (V)

For static fields, there exists a scalar potential V such that E = -∇V.

Vector Potential (A)

For static fields, there exists a vector potential A such that B = ∇ × A.

Poisson's Equation

An equation that is derived by inserting E = −∇V into Gauss’s law, relating the Laplacian of the scalar potential to the charge density.

Laplace's Equation

A simplified form of Poisson’s equation that applies in regions of space where there are no charges (ρ = 0).

Separation of Variables

A mathematical technique used to solve partial differential equations, like Laplace’s equation, by expressing the solution as a product of independent functions, each depending on only one variable.

Multipole Expansion

An infinite series representation of the electrostatic potential due to a localized charge distribution, expressing the potential as a sum of terms with different angular dependencies.

Monopole Term

The first term (l=0) in the multipole expansion, representing the potential of a point charge.

Dipole Term

The second term (l=1) in the multipole expansion. It becomes the dominant term if the net charge of the distribution is zero.

Electric Dipole Moment (p)

A measure of the separation of positive and negative electrical charges in a system.

Gauge Transformation

A transformation that leaves the electric and magnetic fields unchanged.

Lorenz Gauge

A choice of gauge where the divergence of the vector potential is set to r · A = µ0✏0 @V @t .

Retarded Potentials

Solutions to Maxwell’s equations incorporating “retarded” time to account for the delay due to the finite speed of light.

Dielectrics

Materials in which electrons are bound to atoms or molecules and can only be displaced to a limited extent by an external electric field.

Atomic Dipoles

An equilibrium is reached when the electric force due to the external field balances the force of interaction between the nucleus and the electron cloud.

Nonpolar molecules

Some molecules do not have a permanent electric dipole moment. This is the case of the carbon dioxide molecule CO2

Polar molecules

Some molecules have a permanent electric dipole moment, like the water molecule H2O represented on the figure below.

Polarization Vector (P)

The dipole moment per unit volume.

Polarization or Bound Charges

Charges that appear in a material due to the polarization of its molecules.

Polarization Current

A current caused by the changing polarization of a material over time.

The Electric Displacement Vector D

A vector that combines the electric field E and the polarization P of a material.

Linear Dielectrics

Describes materials where the polarization is proportional to the applied electric field.

Electric Susceptibility (χe)

A dimensionless constant that quantifies how easily a material polarizes in response to an electric field.

Permittivity (ε)

A measure of how much a material concentrates electric flux.

Dielectric Constant (εr)

The ratio of a material's permittivity to the permittivity of free space.

Diamagnetic Materials

Materials weakly repelled by a magnetic field.

Paramagnetic Materials

Materials more strongly attracted by a magnetic field.

Ferromagnetic Materials

Materials strongly attracted to magnetic fields, able to retain magnetization even after the external field is removed.

Magnetization Vector (M)

The magnetic dipole moment per unit volume.

Magnetization Currents

Currents produced in a material due to its magnetization.

Auxiliary Field (H)

An auxiliary field used in magnetostatics to simplify calculations in the presence of magnetic materials.

Magnetic Susceptibility (χm)

A dimensionless constant that indicates the degree to which a material will become magnetized in response to an applied magnetic field.

Permeability (µ)

A measure of the ability of a material to support the formation of magnetic fields.

Relative Permeability (µr)

The counterpart to the dielectric constant, representing how much a material concentrates magnetic flux.

Hysteresis

A phenomenon where the magnetization of a ferromagnetic material depends not only on the current applied field but also on its past magnetic history; a source of thermodynamic irreversibility.

Hysteresis Loss

Energy dissipated as heat in a ferromagnetic material due to the lagging of magnetization behind variations in applied magnetic field.

Poynting's Theorem

The rate at which energy contained in the volume V varies.

Plane Wave

An electromagnetic plane wave for which F is uniform over every plane perpendicular to the wave's propagation direction.

Sinusoidal Waves

A wave that has a form of Fk(x,y) = Acos[k(x−ct)+ϕ] + Bcos[k(x+ct)+θ].

Polarization

This describes the direction of an electric field.

Intensity

A measure of the average power per unit area transported by an electromagnetic wave.

Radiation Pressure

The pressure exerted upon any surface exposed to electromagnetic radiation.

Total Charge Density

The total charges (free charges + polarization charges) per unit volume.

Refraction

When light bends when passing from one medium to another.

Skin Depth

The distance it takes for amplitude of a wave to decrease by a factor of e.

Impedance

This is the ratio of transverse E and H, as long as the point is outside of the current generator.

Electric Fields

It may have frequency dependent permittivity.

Dispersion

A method of varying the velocity of the plane with frequency.

Normal Dispersion

In most materials, the index of refraction increases with frequency (or decreases with wavelength).

Anomalous Dispersion

Near a resonant frequency, the drop of index of refraction, with the greatest absorption.

Plasma

Defined as an ionized gas in which positive charges and electrons are unbound.

Active Wire

A conductor the carries the time-varying voltage or current from an inputted circuit to its load.

Telegrapher's Equations

These equations govern the propagation of voltage and current through conductors

Impedance Matching

This is when all the power is absorbed by the load.