# Why electric field at any point inside a charged shell is always zero?

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?

• 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. Feb 12, 2021 at 6:15
• What if the shell is negatively charged and the test charge is positively charged?
– MSKB
Feb 12, 2021 at 6:22
• 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." Feb 12, 2021 at 6:25
• 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. Feb 12, 2021 at 8:23
• 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. Feb 12, 2021 at 9:36