Electric field at and inside a thin hollow sphere with surface charge

[PinkFlamingo]

I'm also stuck on this one. Could someone help me please?

An insulating, thin, hollow sphere has a uniform surface charge density, a.

a) show that the magnitude of the electric field at the surface of the sphere is |a|/E0 (where E0 is the permittivity of free space)

b) a tiny hole is drilled through the shell, thus removing a negligible but of the charge. Show that the magnitude of the electric field in this hole is |a|/2E0

 

[turin]

For part a, consider that the surface of the Earth "looks" flat to us. Alternatively, you can use Gauss' Law and symmetry.

I'd have to think about b for a little bit. I'll leave that to one of the regular helpers here.

 

[kuengb]

For Part b: The original sphere with a hole in it can be viewed as a superposition of the sphere with charge density a and the "hole" (i. e. a little piece of the surface) with charge density -a . So what you do is you compute the fields of the two charge distributions separately and then add them up. The field of the sphere you've computed already (zero inside!), and the field of a surface charge is...

 

[Gokul43201]

If the point is sufficiently close to the surface of the sphere, then even the "little piece of surface" that kueng described looks like an infinite sheet of charge to that point...and the field from an infinite sheet of charge is...