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ahrkron

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ahrkron

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jtbell

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Claude Bile

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Claude.

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Excellent answers; I was actually pondering the same question a few days back.

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the best answer probably is there never has been a case except at the point charge where the potential has been known to blow up or is discontinious.

but if u meant surface charge then it can be very easily proven just take a short line segment across the boundary of the surface charge and calculate the line integral then u can know that as the line get's smaller so does the integrand and hence the potential difference.

note that the integral does exist in the above case though we 'pass' through a 'charge'.remeber we can always integrate function which are discontinious or blow up at finite points the best example would be the greatest integer or mod valued function....

but all these reasons are secondary the most important being experimental verification and nothing else

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although i am wondering whether there is a mathematical proof to show that the potential is continuous everywhere except for point charges.

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i am wondering whether there is a mathematical proof to show that the potential is continuous everywhere except for point charges.

it's the same as that for surface charges as in my last post take a small line and calculate the line integral

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just one last question, will the potential also be discontinuous on a line charge?

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First of all, the original question is:

ahrkron said:

I'm surprised that no one actually pointed out clearly that this is actually not true all the time. While the

Check out here for the detailed derivation using nothing more than Gauss's law.

So no, E-field need not be continuous in all cases.

Zz.

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Oy! You may smack me now.

That's why no one found it puzzling! I need my eyes checked!

Zz.

That's why no one found it puzzling! I need my eyes checked!

Zz.

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About the discontinuity at point charges.

Point charges are really just an approximation. Any real charge distribution, even an electron, takes up a finite amount of space. So the potential in any real situation is continuous.

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Ben Niehoff

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However, a dipole layer imposes a very

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Ben- I'd like to know more regarding dipole layers in regards to cell membranes, do you have a good introductory reference?

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The potential will be continuous at x = 0, but it will not be differentiable and so the field will have a discontinuity.

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