Hello all. I have been trying to learn some Physics in my spare time and I came across Gauss' Law. I've been thinking about different cases and conditions and I have been confused by the actual meaning of Electric flux being 0.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

If I consider a sheet of uniform charge per unit area (sigma) I can calculate the E due to the sheet at an arbitrary distance from it.

I get E = sigma/2Epsilon0

What if I now consider an area which is in the vicinity of the sheet but doesn't actually contain any charge?

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What implications does this have on E?

2. Relevant equations

phi = closed surface integral of E.dA = sum of all charges inside/epsilon0

3. The attempt at a solution

Since the charge inside is 0, flux = 0 and the integral is 0.

This makes sense since on the top side, E is 0 degrees to the surface normal, but on the bottom it's 180 degrees and cos 180 = -1. So the integral is expected to give me 0.

What does this mean? Flux is 0 but clearly E isn't 0.

If I place a test charge in the cylinder I'm considering it will move away from the plates. There IS E.

So flux being 0 doesn't mean E is 0 too?

I could draw parallels with the other Gauss' Law about magnetic flux. It's always 0 right? It's physical implication was that there is no magnetic monopole. Each B field line we think of must be either a loop or be extended to infinity.

I tried to look at some general meaning of flux. I found that flux is sum of all inflow - sum of all outflow.

So, this result when we look at a cylinder far away from the sheet is expected as the flux in and out are equal. This means ther are no field lines being "created" or "destroyed" i.e. there is no charge.

But then when I started thinking about Faraday cages I got really confused.

Does this mean that this law can never tell us the E ever. We can't calculate the electric field strength in a region using this law. Since, when we use this law, we don't consider other charges that could be nearby?

Like in this case we didn't look at the fact that there was a charged sheet nearby.

Is there any truth to this? Or am I doing it wrong? amidoinitrite guise?

If I have, say, a point charge somewhere. And very far away I take a Gaussian sphere. The sum of all charges in is 0. So flux is 0. But the E isn't 0 since if I place a test charge there, it will experience a force.

tl;dr

Does this mean that this law can never tell us the E ever.

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# Homework Help: Gauss' Law and it's meaning

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