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Why is E for the infinite wire dependent on distance, but not the distance for the infinite sheet. Wouldn't the E get smaller the farther away from the infinite sheet??? This is not a HW question.

- Thread starter robbondo
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- #1

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Why is E for the infinite wire dependent on distance, but not the distance for the infinite sheet. Wouldn't the E get smaller the farther away from the infinite sheet??? This is not a HW question.

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For the wire the reinforcement is only partial. A cylindrical surface constructed in symmetry with the wire uses Gauss's law as

2(pi)rlE

so the wire's electric field is inversely proportional to the radial distance from the wire.

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If the extended sheet is a conductor, the electric field within it is zero. You can construct the pillbox for the sheet with an end placed just inside the conducting sheet, and the other just outside it. The cylinder itself is perpendicular to the sheet. The only contribution here is due to the E-field through the outside end of the pillbox.

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Claude Bile

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Claude.

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a point charge falls off as 1/r^2;

an infinite line of charge (composed of an infinite line's worth of charges) falls of as r(1/r^2)=1/r;

an infinite plane of charge (composed of an infinite plane's worth of charge) falls of as r^2(1/r^2)=constant.

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Claude Bile

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I agree, Physicians are weird.Like I actually overheard someone say in the hallway of our physics building today "that's why physicians are so weird" lol~

Us Physicists however are normal, balanced folk!

Sorry I couldn't resist.

Claude.

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this has to do with the fundamental reason why there are inverse-square laws in a universe with 3 spatial dimensions. it has to do with the concept of "flux" or "flux density" of stuff and equating "field" to "flux density" (perhaps with a scaling constant that depends on our anthropocentric unit systems).Why is E for the infinite wire dependent on distance, but not the distance for the infinite sheet. Wouldn't the E get smaller the farther away from the infinite sheet??? This is not a HW question.

check out

http://en.wikipedia.org/wiki/Inverse-square

http://en.wikipedia.org/wiki/Flux

http://en.wikipedia.org/wiki/Gauss's_law

you can go through the nasty double integrals, but think of it conceptually a little.

take a look at a point charge as a little particle. as you move away from it, that particle appears smaller to you in

now take a look at an infinite line of charge. as you move away from it, that infinite line appears smaller (more precisely "thinner") to you in

now take a look at an infinite plane of charge. as you move away from it, how does it appear smaller? if you're in empty space, except for that infinite plane of charge, how can you tell that that infinite plane of charge is 1 kilometer away from you or 1 lightyear away from you?

more properly, think of all 3 of these geometries as emitting "flux" whatever their "stuff" of interaction is. for illustration let's think of flux as emitted energy of some radiative source and "flux density" as the

here at Earth, we get about 1300 watts of sunlight falling on every square meter, but you might expect it to be more when you're on Mercury or less when you're on Mars. knowing that we are about 150 billion meters from the Sun and that the surface area of a sphere (in our 3-D existance) is [itex] 4 \pi r^2 [/itex] (for radius

so what would the intensity be if you got in a spaceship and doubled your distance from the Sun? the Sun's total output remains the same 3.7 x 10

a point source emits a finite amount of total flux outward in all 3 spatial dimensions will have the flux density increase in proportion to the reciprocal of the square of the distance because the size of the encapsulating sphere is reduced directly in proportion to the square of the distance.

now imagine an infinite line of charge. each meter of length of that infinite line of charge is emitting a fixed amout of flux. because of symmetry, the flow of flux must be perpendicular to the line and it flows out spreading in only 2 dimensions. for each meter of length, you can imagine a cylinder of the same length and radius

now imagine an infinite plane of charge. each

a wordy, but i hope rigorous answer.

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