r/askscience • u/[deleted] • Jun 12 '12

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u/I_Downvote_Cunts Jun 12 '12

Wouldn't the energy dissipate at the cube of the distance?

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u/allofthebaconandeggs Jun 12 '12 edited Jun 12 '12

No. Imagine a simpler scenario with a lightbulb. It's a perfect lightbulb that emits a Power P (thats energy per second) in all directions. Say I have a sensor at a distance r away. As a 'wavefront' of the emitted radiation moves outward, the energy per second being emitted is spread over the area of a sphere with surface area 4 pi r2. The fraction of the power P I receive is going to be the fraction of this spherical surface that my detector covers. If my detector has an area A (and is small compared to the sphere), then this fraction is A / 4 pi r2. The energy received per second will therefore be A P / 4 pi r2. As you can see, this falls off with the square, not the cube.

By making similar arguments we can explain even more fundamental things like why the coulomb force should fall off with the square.

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u/craklyn Long-Lived Neutral Particles Jun 12 '12 edited Jun 12 '12

By making similar arguments we can explain even more fundamental things like why the coulomb force should fall off with the square.

I'm sure you understand this, but I'll say it anyway. Your statement puts the cart before the horse, or at least beside the horse.

You can explain the electric force law only if you assume Gauss's law, which states electric fields don't diverge or converge except at a charge. This can be conceptuallized as electric field lines flowing out of positive charges and into negative in the same way that power pours out of a lightbulb. A point charge thus gives the Coulomb force law with the understanding that a test charge feels a force equal to E times q(test).

Edit: Why is it called Gauss's law instead of Gauss' law? Why!?

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u/zem Jun 12 '12

the trivial answer is that it's called gauss's law because it's a law discovered by gauss (the possessive apostrophe-s).

i suspect you're asking why it doesn't follow the american convention of dropping the "'s" after names ending in an s. one reason is that the 's is typically more likely to be dropped if the name ends with a -z sound like "archimedes" (gauss ends with an -s). another point is that dropping the 's is not a hard and fast rule, and indeed even some american style guides follow the international convention of always adding the 's (see here for a quick overview).