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I Love Physics

Heaviside And Gibbs Deserve Some Of Maxwell's Fame... The name "Maxwell's equations" honours the greatest physicist between Newton and Einstein. But Clerk Maxwell did not discover his eponymous equations; when Maxwell was alive, vector calculus was unknown. In particular, the curl and divergence operators were unknown.

We owe Maxwell's equations to Oliver Heaviside, the self-taught British electrical engineer who discovered an immense amount of EMF theory, laid the groundwork for radio and TV broadcasting, and discovered vector calculus and the Laplace transform.

"Heaviside did much to develop and advocate vector methods and the vector calculus. Maxwell's formulation of electromagnetism consisted of 20 equations in 20 variables. Heaviside employed the curl and divergence operators of the vector calculus to reformulate 12 of these 20 equations into four equations in four variables (B, E, J and ρ), the form by which they have been known ever since."
http://en.wikipedia.org/wiki/Oliver_Heaviside#Innovations_and_discoveries

If 4 equations in 4 variables strikes you as much less unwieldy than 20 equations in 20 variables, you are in good company. We also owe vector calculus to the great American scientist Willard Gibbs:
http://en.wikipedia.org/wiki/Josiah_Willard_Gibbs#Vector_analysis

Gibbs's vector calculus reformulation of electrodynamics did not become well known until his student E B Wilson reworked Gibbs's lecture notes into an undergraduate text, published in 1901.

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freeed

Hmm...I didn't realize Maxwell predated vector calculus. Still, if the 20 equations he did come up with first describe magnetism and electricity he deserves credit for that. A mathematical reformulation is not a fundamental change in theory.
An interesting fact is that the cross product operation doesn't work in every dimension, only in 3D and 7D!! See, e.g.:
http://math.stackexchange.com/questions/706011/why-is-cross-product-only-defined-in-3-and-7-dimensions

consa01 · 70-79, M

There are deep mathematical and physical reasons why our universe has 3 spatial dimensions. John Barrow explicated some of those reasons in his 2002 The Constants of Nature. Barrow's work is partly based on some 1950s articles by the British physicist Gerald Whitrow. But it is fascinatingly true that 3 spatial dimensions work better, and are more mathematically interesting, than any other number of spatial dimensions.

consa01 · 70-79, M

I prefer that Maxwell's equations be formulated in term of natural units, in which case c=1. Setting the permittivity of free space to 1 makes 4pi disappear. I also prefer rho=J=0. No current, no charge, all in a vacuum. All that is left, other than "the curl of both vector fields is zero, the divergence of one field equals the gradient of the other field" is a single pesky minus sign. I would love it if someone would leave a comment explicating that minus sign.

atenra11

so consa and freed, what books did you study EM from....

High School, First Year, or Second Year stuff.....

And you also need to remember that in the 1910s and 1920s you could get a BSc in Physics and never see Maxwell's Equations...

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atenra11

You're probably thinking of:
A Student's Guide to Maxwell's Equations - Fleisch - Cambridge 2008

Gentle might be:
a. PSSC Physics 1960 or 1965
b. Sears College Physics - Addison-Wesley
c. Bueche - Physics for Science and Engineering - McGraw Hill
d. Halliday and Resnick - Physics - 3ed - 1970s
e. Purcell - Berkeley Physics Series Volume Two - 1965
f. Student's Guide to Maxwell's Equations - Fleish

maybe some older Jerry Wilson Physics stuff that's maybe a bit easier than Bueche and Sears, and more like a 70s 80s level of PSSC

i think 70s Halliday and Resnick is probably the most leisurely read but on a pretty advanced level..... but i wouldnt play with any of the 90s editions just for the lousy artwork and cluttered graphic design.

I think the books got easier in the 70s and 80s from the 60s incarnations
I think HR omitted AC Circuits in early editions and later expanded it, since they felt a lot of that stuff was in other textbooks, and i think as Electronics books were on their last legs of the golden era of the 70s, they beefed up their electronics, and always had beautiful explanations and graphics in their older editions......

then the paper got shiny and the graphics got computer designed and full colour where i think black and white and two tone was perfectly adequate and easy on the eyes.

Now i think textbook people try to add colour and flash as a way of grabbing attention desparately. Gianacoli is bad for that, and any physics book that has photos of athletes, esp on the cover...

consa01 · 70-79, M

Fleisch's book on Maxwell's equations is indeed what I had in mind.

http://www.amazon.com/A-Students-Guide-Maxwells-Equations-ebook/dp/B0018O6R8G

atenra11

i hear that offers one of the least painless ways of getting the math skills for EM, stuff that you may or may not learn well in second year math

from what it sounds like, the book replaces any knowledge of calculus III and IV and you just zoom into the basics

Theocrat

True.
Especially Heavyside, he deserves FAR more attention than he currently recieves.

consa01 · 70-79, M

I am not sure if Heaviside finished high school. In science and math, he was almost entirely self-educated. I agree with those who say he was the greatest electrical engineer of all time. First rate mathematicians proved decades later that his operator methods could be rigorously derived. Heaviside had colossal intuition.

Theocrat

At the end of the day, intuition is a lot more valuable quality in a scientist than it is given credit for being.
Heaviside was once asked to establish how operational calculus works. He replied, "I don't know." When asked why he still uses such a method, he replied: "I don't know how my digestive system works. Does that mean I have no right to eat?"
Besides, he would not have needed schooling; He had Wheatstone for uncle ;)

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