Maxwell' Equations: Physics E & M

Gauss's Law for Electricity

Electric charges produce electric fields and the electric flux leaving a region equals charge enclosed divided by epsilon0

Gauss's Law for Magnetism

Magnetic fields have no beginning or end and the net magnetic flux through any closed surface is zero because magnetic monopoles do not exist

Faraday's Law of Induction

A changing magnetic field induces an electric field which produces a non conservative electric loop

Ampere Maxwell Law

Magnetic fields are created by electric currents and by changing electric fields Maxwell's correction makes electromagnetic waves possible

Electric Flux

Total amount of electric field passing through a surface equals integral of E dot A

Magnetic Flux

Total magnetic field passing through a surface equals integral of B dot A

Divergence of a Field

Measures how much a field spreads out from a point positive means source negative means sink zero means no net outflow

Curl of a Field

Measures how much a field circulates around a point nonzero curl means twisting or rotation of field lines

Displacement Current

The term epsilon0 times dE dt that allows Ampere's Law to work even in regions with no charge flow

Electromagnetic Wave

Self sustaining oscillating electric and magnetic fields that propagate at speed c in vacuum

Speed of Light from Maxwell

c equals 1 over sqrt of mu0 times epsilon0 showing light is an electromagnetic wave

Induced EMF

Voltage generated by changing magnetic flux as described by Faraday's Law

Magnetic Field from Currents

Steady electric currents create magnetic fields as in original Ampere's Law

Nonexistence of Magnetic Monopoles

B field has zero divergence meaning no isolated magnetic charges

Integral Form Faraday Law

The line integral of E around a closed loop equals negative rate of change of magnetic flux through the loop

Integral Form Ampere Maxwell

The line integral of B around a closed loop equals mu0 times current enclosed plus mu0 epsilon0 times change in electric flux

Electric Field

Electric force per unit charge measured in newtons per coulomb generated by charges or changing magnetic fields

Magnetic Field

Field that exerts force on moving charges and magnetic dipoles generated by currents or changing electric fields

Continuity Equation

Expresses conservation of charge by relating change in charge density to divergence of current density

Charge Density

Rho represents how much electric charge exists per unit volume acts as the source term in Gauss's Law

Current Density

J vector describes flow of charge per unit area contributes to magnetic fields through Ampere Maxwell Law

Electrostatic Condition

When fields do not change with time curl E equals zero so electric field is conservative

Quasistatic Approximation

Assumption that fields change slowly enough to ignore radiation terms useful in many circuits

Poynting Vector

Vector E cross B that gives energy flow direction and rate in electromagnetic fields

Energy Density EM Fields

Energy stored in E and B fields equals epsilon0 E squared over 2 plus B squared over 2 mu0

Boundary Conditions E Field

Tangential electric field is continuous across boundaries unless surface charge is present normal component changes with surface charge density

Boundary Conditions B Field

Tangential magnetic field changes with surface current normal component is continuous because no magnetic charges exist