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We know that electric field at any point inside a charged shell is always zero since there is no charge inside the shell other than the periphery. But why is that?

Being curious I once tried to find out if it is really zero or not using coloumb's law😅. I drew a circle considering origin as the centre. Then I marked total 20 points on the circle, 10 points on each side of the y-axis such that the other 10 points are exactly the image of them(each points ar representing negative charges). Then I took another point on the positive y-axis. Considered that a test object(positive charge) is placed on the y-axis. After calculating the electric field I found that the net electric field is acting towards the positive y-axis(0→∞). The reason behind taking circle is that I thought if infinite numbers of similar circles are taken to form a sphere(hollow) it would form a shell which I have imagined. So the field will increase rather than goimg towards zero.

Can someone explain whether I was correct or not in terms of the process I used?

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  • $\begingroup$ Are you asking about electric field lines from a charge don't like to run into another charge of the same polarity and will tend to veer away from it instead? Because if you surround a point surrounded by charges of the same polarity, none of the field lines from them will want to go towards the other charges (i.e. inside) and will all point away instead. $\endgroup$
    – DKNguyen
    Feb 12 '21 at 6:15
  • $\begingroup$ What if the shell is negatively charged and the test charge is positively charged? $\endgroup$
    – MSKB
    Feb 12 '21 at 6:22
  • $\begingroup$ That's changing your initial scenario (or at least what I interpreted your initial scenario) which was just a shell of charges and nothing else, in which case, it won't be zero. To be honest, I am not sure what you mean by "We know that electric field at any point inside a charged shell is always zero since there is no charge inside the shell other than the periphery." $\endgroup$
    – DKNguyen
    Feb 12 '21 at 6:25
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    $\begingroup$ Why is that? When you integrate, at any point inside, the field contributions (from Coulomb’s Law) due to every infinitesimal bit of charge on the spherical shell, you get a net field of zero. $\endgroup$
    – G. Smith
    Feb 12 '21 at 8:23
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    $\begingroup$ Your initial statement that the "electric field at any point inside a charged shell is always zero since there is no charge inside the shell" is not correct. This is an ill-posed problems. $\endgroup$
    – my2cts
    Feb 12 '21 at 9:36
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Alright...so firstly the electric field is zero only inside a charged conducting shell.Now,to the question as to why electric field must be zero inside a conductor,is because net charge cannot exist inside it.This is because in the influence of an external electric field(due to a positive charge let's say)towards right the positive charges inside the conductor shifts towards the right and the negative charges shift towards left..but this creates a very strong internal electric field inside the conductor(opposite to the direction of the external field) which in a very short time becomes equal to the external field and cancels it out.So, whatever charge you give the conductor from outside would just exist uniformly over the outer surface.SO, in electrostatic condition if a net charge was to exist inside a conductor would cause an electric field which would move some of charges...so its not possible. Also..since you are talking about a shell it's essentially empty inside so charges can't possibly stay in an empty space.

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    $\begingroup$ The electric field is zero only inside a charged conducting shell. That’s not true. The electric field is zero inside a nonconducting shell with uniform surface charge density. $\endgroup$
    – G. Smith
    Feb 12 '21 at 8:08
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    $\begingroup$ @G.Smith Only for a spherical shell. $\endgroup$
    – my2cts
    Feb 12 '21 at 9:43
  • $\begingroup$ Yes...if it's a non conducting shell electric field should be zero ...because charges cannot be present in empty space $\endgroup$
    – Soura Deep
    Feb 12 '21 at 10:49
  • $\begingroup$ @my2cts also true inside an infinitely long thin cylinder. $\endgroup$ Feb 23 '21 at 4:08

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