EECE 557 Study Sheet Hints

BASIC VECTOR CALCULUS

"Flux" is the integral of a vector field over a surface: how much of the vector "flow" goes thru the surface?
"Circulation" is the integral of a vector field around a closed path: to what degree does the vector field go in a loop?"
"Divergence" tells whether a vector field has a source or sink at the point of evaluation
"Curl" tells whether a vector field has any rotation (spin, whirl-pool-ness) at the point of evaluation
"Gradient" gives the value and direction of the maximum slope of a scalar field at the point of evaluation

ELECTROSTATICS

TBA

MAGNETOSTATICS

Magnetic flux density: like electric flux density, except there are no magnetic monopoles
Lorentz Force Law

Energy is mv²
Path of charged particle: think of particle accelerators and Mass spectrometers
Force between 2 currents: where the magnetic fields add, their sources repel; where they cancel, their sources attract

Inductance

If you can't count the number of loops, use energy stored to calculate L
Mutual inductance is reflexive; use as the flux source the one that's easiest to calculate

Magnetic Materials and Boundary Conditions

The derivations split normal and tangential fields to make it easier to solve for them. This is a math trick.
Permeability is a measure of both how readily magnetic dipoles of a material respond to an applied magnetic field, and how much magnetic energy can be stored in the material relative to free space.
Ferrimagnets have very low conductivity
Magnetic dipoles exist all the time and align (or not) in applied H. Electric dipoles (usually) do not exist until E is applied, but grow stronger with greater E.

TIME-VARYING ELECTROMAGNETIC FIELDS

Faraday's Law

Current flows to oppose the change in total magnetic flux through a conducting loop.
If you can't find the "loop" but some part of the circuit has a velocity, use vxB
You can always use d/dt (total flux)

Displacement Current

E -> H -> E forms a closed loop; you can check your work by going all the way 'round.
Displacement current is proportional to frequency and very much smaller than conduction current unless the frequeny is high (AM radio or above.)

Maxwell's Equations

Gauss: the source (or sink) of electric field is charge
Ampere: magnetic fields wrap around (are induced by) steady electric currents and time-varying electric fields
Faraday: electric fields wrap around (are induced by) changing magnetic fields
There are no magnetic monopoles worth worrying about in EM design.
The source of electric current is time-varying electric charge, or, net charge must decrease at a point if electric current is leaving that point.

Last revised 27 October, 2003, by Ruth Douglas Miller