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- Thread starter Observable
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Observable said:

well, radiation is nothing more than oscillating electric and magnetic fields, so let's look at maxwell's equations in vacuo...

div

div

since the divergence of the electric field is zero (in vacuum), it is "solenoidal," that is, it's purely rotational, and in that situation, you can't use scalar potential--you have to use vector potential.

now it's in the same boat as the B-field! it's divergence is always zero (so long as we don't find any magnetic monopoles!), so it can't have an associated scalar potential.

...did that help?

now...i'm unsure of how the situation changes once charges are introduced. ...is that your question?

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Brad Barker said:since the divergence of the electric field is zero (in vacuum), it is "solenoidal," that is, it's purely rotational, and in that situation, you can't use scalar potential--you have to use vector potential.

Just to point what seemed to me as an incorrect reasoning:

Uniform electric field has zero divergence and is consequence of a well defined scalar potential V(X,Y,Z) = kX, for instance.

Best regards,

DaTario

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DaTario said:Just to point what seemed to me as an incorrect reasoning:

Uniform electric field has zero divergence and is consequence of a well defined scalar potential V(X,Y,Z) = kX, for instance.

Best regards,

DaTario

right! my mistake.

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from pg. 43 of arfken and weber...

"If we have the special case of the divergence of a vector vanishing, the vector...is said to be solenoidal.... When a vector is solenoidal it may be written as the curl of another vector known as the vector potential."

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Hans de Vries

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Observable said:

This is

The separation of E in dV/dr and dA/dt is unfortunately often not given.

(Jackson doesn't show it for instance in Chapter 14 on Radiation by moving charges)

You can find the formulas online here:

http://fermi.la.asu.edu/PHY531/larmor/

see formula 15 for dA/dt and formula 16 for dV/dx. The dotted beta (v/c) is

the accelaration (a/c) which gives the radiation terms. You can simplify the

formula by setting beta itself to zero (v<<c).

You also should be able to find them here:

www.pas.rochester.edu/~dmw/phy218/Lectures/Lect_67b.pdf

At least when rochester.edu is back up again (maintanance?) at page 28.

Regards, Hans

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- #8

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I once used the radiation gauge and, as I understand it, it represents one possible way of expressing field situations. V and A concepts provide some amount of redundancy, and this gauge choice is a way of fixing this redundant system of language.

Best Regards,

DaTario

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