Fall 2015

EE 671: Electromagnetic Theory and Applications

Zhengqing (ZQ) YunHawaii Center for Advanced Communications (HCAC)

Fall 2015

Faraday’s Discovery - 1831

• Whenever a magnetic force increases or decreases, it produces electricity;

• The faster it increases or decreases, the more electricity it produces.

Fall 2015

Maxwell’s Comments

• As I proceeded with the study of Faraday, I perceived that his method of conceiving the phenomena (of electromagnetism) was also a mathematical one, though not exhibited in the conventional form of mathematical symbols. I also found that these methods were capable of being expressed in the ordinary mathematical forms, and thus compared with those of the professed mathematicians.J. C. Maxwell, A Treatise on Electricity and Magnetism, p.ix, vol. I, Dover, 3rd Ed., 1954 (1st Ed., 1873.)

Fall 2015

A new concept appeared in physics, the most important invention since Newton’s time: the field. It needed great scientific imagination to realize that it is not the charges nor the particles but the field in the space between the charges and the particles that is essential for the description of physical phenomena. The field concept proved successful when it led to the formulation of Maxwell’s equations describing the structure of the electromagnetic field and governing the electric as well as the optical phenomena.(Einstein & Infeld)

I have also a paper afloat, with an electromagnetic theory of light, which, till I am convinced to the contrary, I hold to be great guns. (Maxwell)

One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than we originally put into them.(Hertz)

Fall 2015

Maxwell’s Equations

S

SdBt

dE

S

Sdt

DJdH

0S SdB

qSdDS

t

BE

t

DJH

D

0 B

Faraday

Ampere

Gauss

Source: q, , J

What it means really to understand an equation that is, in more than a strictly mathematical sense was described by Dirac. He said: “I understand what an equation means if I have a way of figuring out the characteristics of its solution without actually solving it.” A physical understanding is a completely unmathematical, imprecise, and inexact thing, but absolutely necessary for a physicist. Feynman’s Lectures on Physics

Fall 2015

Maxwell’s Equations

S

SdBt

dE

S

Sdt

DJdH

0S SdB

qSdDS

t

BE

t

DJH

D

0 B

Faraday

Ampere

Gauss

Source: q, , J

Fall 2015

Maxwell’s Suggestions

Fall 2015

Maxwell’s “Laws”

• The slope of a scalar function has no curl.• The curl of a vector function has no

convergence.• The convergence of the slope of a scalar

function is its concentration.• The concentration of a vector function is

the slope of its convergence, together with the curl of its curl.