The unification of electric and magnetic forces

Not sure exactly what you're asking, but http://en.wikipedia.org/wiki/Electromagnetics" [Broken] might be a good starting point.

Electric and magnetic fields are closely related, obviously, since each one generates the other. Is that what you're asking about?

Or are you wondering about the fact that they are actually the same force from two different points of view according to relativity?

 

Maxwell's equations can be found http://en.wikipedia.org/wiki/Maxwell%27s_equations" [Broken]. I'm not sure what you mean by the Maxwell theory, unless that just means classical electromagnetics. The link I posted before discussed electromagnetics in general. It is a broad subject; you could spend years studying it.

Don't worry about relativity, I was just trying to figure out what you were asking.

 

I think he meant historically, since electric and magnetic forces were originally thought to be separate forces, which were later unified. When was it discovered that they were the same?

 

"Could someone introduce me some docs about the unification of electric and magnetic forces?"
-- from first entry in this topic

How about the late Chris Zafiratos' derivation of the magnetic field from the electrostatic Coulomb field[tex]:^1[/tex]

[tex]\vec{F}=\frac{k q_{1} q_{2}}{\vec{r^2}}[/tex]

and asserting from experimentation that between two like charges q with equal (parrallel) velocities separated by r that the force is reduced by[tex]:^2[/tex]

[tex]\vec{F}=\frac{k q_{1} q_{2}}{\vec{r^2}}(1 - \frac{v^2}{c^2})[/tex]

then multiplies this out and derives to[tex]:^3[/tex]

[tex]\vec{F} = \frac{k q_1 q_2}{\overset{\rightharpoonup }{r}_{12}^2}-\frac{k q_1
q_2}{\overset{\rightharpoonup }{r}_{12}^2}(\frac{v^2}{c^2})[/tex]

[tex]\vec{F}= \vec{F_{e}} + \vec{F_{M}}[/tex]

Where

[tex] \vec{F_{M}}= -\frac{k q_{1} q_{2}}{\vec{r^2}}( \frac{v^2}{c^2})[/tex]

and

[tex] \vec{F_{e}}= \frac{k q_{1} q_{2}}{\vec{r^2}}[/tex].



Could you explain if the first equation can be derived from specal relativity (ie the (1 -[tex]\beta^2[/tex]) term? or point me to text with similar reasoning and explanations?

[1] Purists might prefer [tex]\frac{k q_1 q_2 \hat{r} }{r^3}(1-\frac{v^2}{c^2})[/tex]
[2] Physics, Chris Zafiratos C1976 John Wiley & Sons pp 710-712 ( first edition)
[3] I would show you the whole derivation and his conclusion for the magnetic force in Guassian and SI units if I had more time.

 

If you go to Google book search, try looking for the old papers of Faraday and Ampere and Euler, also search "correlation of the forces of nature", "identity of the imponderables".

 

But how do you search for a mathematical equation? Do you use Tex, MathML, ... I anticipate the symantic web when we will search ideas and concepts, not type setting and encodings, etc !

There are two things that bother me with Zafiratos' spectacular but arbitrary assertion. If he were using the Taylor series approximation

[tex](1-x)^n\approx 1-\text{nx}[/tex]

for either

[tex]\frac{1}{c^2-\upsilon ^2}[/tex] or [tex]\frac{1}{\sqrt{c^2-\upsilon ^2}}[/tex]


then

[tex]\frac{1}{c^2-\upsilon ^2}\approx \frac{v^2}{c^2}+1[/tex]

and

[tex]\frac{1}{\sqrt{c^2-\upsilon ^2}}\approx \frac{v^2}{2 c^2}+1[/tex]

Yet Zafiratos uses

[tex]\frac{- v^2}{c^2}+1[/tex]

It is the minus sign that intrigues me.

Plus the fact that when v = c the whole expression goes to F = 0! ( ie at the speed of light the electro static force is zero).

(Maybe this is the wrong forum for this type of question? Does any one have a suggestion? By the way, "correlation of the forces of nature" is an excellent Internet search string! Thanks! I am just now trying "identity of the imponderables" and the 1843 edition of "New Philosopy of Matter")

 

Hi,

I think that Paul Dirac, Maxwell, Larmor have developed many mathematical models of the interaction of electric and magnetic fields. Larmor is very mathematical, way beyond anything I can follow easily.

DA