- #1

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- David J Griffiths

But how s it valid for some conductor like →

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- Thread starter Shreyas Samudra
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- #1

- 166

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- David J Griffiths

But how s it valid for some conductor like →

- #2

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- #3

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1) Maxwells equations.

2) Electrostatic: ##J=0##, ##d\rho/dt=0##, ##dE/dt=0##, ##dB/dt=0##

3) Conductor: ##J=\sigma E##

Assume there is charge in the interior. Then by Gauss law there is an E field in the interior. Then by assumption 3) there is a current. This contradicts assumption 2). Therefore there can be no charge in the interior.

- #4

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if some charge is given to an arbitrarily shaped conductor, it will surface and regardless of everything; the field inside will be zero and the surface will be equipotential

- #5

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please reply

somebody !!

somebody !!

- #6

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$$\sigma \vec{E}=\vec{j}=0 \; \Rightarrow \; \vec{E}=0.$$

The electric charge density at every point is given by Gauss's Law (Heaviside-Lorentz units)

$$\vec{\nabla} \cdot \vec{E}=\rho.$$

Since ##\vec{E}=0## inside the conductor also ##\rho=\vec{\nabla} \cdot \vec{E}=0## inside the conductor. So if the conducting body is overall charged, the charge must be on its surface.

Caveat: To be more accurate, of course microscopically the entire body consists of charged particles (atomic nuclei and electrons). So there are charges inside the body but they are compensating each other precisely in the static case, when looked from a macroscopic (coarse-grained) point of view. So within macroscopic electrodynamics the macroscopic charge distribution vanishes in conductors for electrostatic situations.

- #7

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so #4 is right ?

- #8

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if some charge is given to an arbitrarily shaped conductor, it will surface and regardless of everything; the field inside will be zero and the surface will be equipotential

- #9

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by the way can you put this physically , I don't know this mathThe electric charge density at every point is given by Gauss's Law (Heaviside-Lorentz units)

⃗∇⋅⃗E=ρ.

- #10

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Only in the electrostatic case, yes. This does not hold in magnetostatics or electrodynamics.

if some charge is given to an arbitrarily shaped conductor, it will surface and regardless of everything; the field inside will be zero and the surface will be equipotential

- #11

SammyS

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Yes. The surface is equipotential.

if some charge is given to an arbitrarily shaped conductor, it will surface and regardless of everything; the field inside will be zero and the surface will be equipotential

That does not mean that the surface charge is uniformly distributed.

- #12

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Then we should have current over the surface, as its made of conductor, does that happen in steady state ?Yes. The surface is equipotential.

That does not mean that the surface charge is uniformly distributed.

It won't be electrostatics then !

- #13

SammyS

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I didn't mention current, nor did I imply it.Then we should have current over the surface, as its made of conductor, does that happen in steady state ?

It won't be electrostatics then !

The surface charge density is not one uniform value over the whole surface. It varies from location to location, but it is static.

- #14

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that means it is equipotentialI didn't mention current, nor did I imply it.

The surface charge density is not one uniform value over the whole surface. It varies from location to location, but it is static.

- #15

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Yes.that means it is equipotential

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