- #1
bodensee9
- 178
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Hello
I have a conceptual question about the following. Suppose I have a spherical shell with charge density [tex]\sigma[/tex] that is uniformly distributed throughout its surface. My shell has radius a. Then I cut a little circular piece of radius b with b << a. Then I know that my electric field at the center of this little hole is given by [tex]2\pi\sigma[/tex], because I can treat my shell with hole as a perfect shell, with [tex]E = 4\pi\sigma[/tex] going outwards and then a little piece with [tex]2\pi\sigma[/tex] going inwards (and then I add the two). So then at the center of this sphere, I would have a field of magnitude
[tex]2\pi\sigma[/tex] going inwards because inside the shell I have no field? Thanks.
I have a conceptual question about the following. Suppose I have a spherical shell with charge density [tex]\sigma[/tex] that is uniformly distributed throughout its surface. My shell has radius a. Then I cut a little circular piece of radius b with b << a. Then I know that my electric field at the center of this little hole is given by [tex]2\pi\sigma[/tex], because I can treat my shell with hole as a perfect shell, with [tex]E = 4\pi\sigma[/tex] going outwards and then a little piece with [tex]2\pi\sigma[/tex] going inwards (and then I add the two). So then at the center of this sphere, I would have a field of magnitude
[tex]2\pi\sigma[/tex] going inwards because inside the shell I have no field? Thanks.