Perfect Differential: What Is It?

[mess1n]

Hey, I'd really appreciate if you could read the following transcription from my textbook and let me know what exactly a perfect differential is, because I have no idea!

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W = q $$\int \textbf{E} . \textbf{dr}$$ [ the work done in moving a charge q (sorry about the formatting, it's meant to all be one line)]

... can be written as the 'perfect differential' d(-1/r) when E is given by Coulomb's Law:

d(-1/r) = $$\frac{\textbf{r} . \textbf{dr}}{r^{3}}$$

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Cheers guys,
Andrew

 

[tiny-tim]

Hi Andrew!

(have an integral: ∫ )

I means that it has an easy anti-derivative:

∫ E.dr = ∫ r.dr / r³ = ∫ d(r²/2) / (r²)^3/2 = …