E-field & hollow non-conducting sphere

1. Nov 10, 2013

CsLevi

I know that the E-field around a hollow non-conducting sphere charged with Q charge comes immediately from Gauss' Law but I'm wondering what the situation is if we somehow go inside the material, we make a very small hole through the material of the sphere and go inside it. What would there be the E-field?

2. Nov 10, 2013

Meir Achuz

If the charge is a uniform surface charge, then the field inside would be zero by Gauss's law.

3. Nov 11, 2013

CsLevi

Even inside the hole when being half outside, half inside the sphere?

4. Nov 11, 2013

Meir Achuz

Inside the hole, at radius R, the E field is one half Q/R^2.
The E field goes from Q^2/R to zero as r decreases through the hole.
The decrease in E takes place in a distance of the order of \Delta r=d, where d is the diameter of the hole.

5. Nov 11, 2013

CsLevi

So right on the surface it would be E = Q/ (4R^2 pi * epsilon_0), but when going through the hole, right inside the sphere it is already 0. Does it follow from Gauss' Law to be more obvious? E.g.: we choose the Gaussian sphere with radius R such that it goes through the charge layer. Thus, the total amount of charge inside the Gaussian sphere is Q/2 so E inside the hole is indeed 1/2 * Q/ (4R^2 pi * epsilon_0).

6. Nov 11, 2013

Meir Achuz

That happens anywhere at the surface, not just at the hole.

7. Nov 12, 2013

CsLevi

Interesting, thanks!