# Gauss's law to solve for electric field.

#### playoff

An infinitely long line charge with a linear density +λ inside an infinitely long cylinder of radius R and area density -λ/(2pi*R).

So if I set up a cylindrical Gaussian surface with length L, the positive charge inside the surface would be λL and negative charge inside the surface would be area density multiplied by area so -λ/(2pi*R)*(2pi*RL) => -λL, cancelling each other out no matter what.

But the problem is that electric field has to exist, because I am supposed to compare this derived electric field with experimental data.

Did I miss out on something?

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#### Simon Bridge

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What does the experimental data tell you?

#### playoff

Well there definitely seems to be an existing electric field according to my data. I should have added this: I am supposed to find the size of lambda that would generate the electric field recorded from the lab. But since electrical field is always 0, there can't be a lambda that would fit my experimental data.

Could someone evaluate whether I have used Gauss's law correctly and came up with a correct answer?

#### Simon Bridge

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If the coaxial model you are using is a good fit to the experiment, then the electric field should be very small outside the coax.
That is why I asked you what the data is telling you. Is the electric field almost zero?

It is unlikely that you actually have an infinitely long bit of coax in the lab though ... so you will not get an exactly zero field.

The answer to the question as you wrote it down is, as you have pointed out, there is no value of lambda that can give the measured field.
If you have missed something, it was in something you have not told us yet.

#### rude man

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Hey, how did you get that lambda into your post? I mean the Greek letter.

Last edited:

#### rude man

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Are you sure you were'nt supposed to find the E field between the inner wire and the outer shield?

#### Simon Bridge

Science Advisor
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You mean $\small{\lambda}$? Same way as always - LaTeX.
But it looks like the first post may have used the "insert unicode" trick.

#### Orodruin

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Are you sure you were'nt supposed to find the E field between the inner wire and the outer shield?
I would like to second this question. Where exactly did you measure the field?

#### Simon Bridge

Science Advisor
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It's my bet for the missing information - yes.

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