E-field & hollow non-conducting sphere

In summary, the E-field inside a hollow non-conducting sphere charged with Q charge is zero if the charge is a uniform surface charge, according to Gauss's Law. Even inside a small hole within the material of the sphere, the E-field is still zero at the surface. However, as one moves through the hole, the E-field gradually decreases from Q^2/R to zero within a distance approximately equal to the diameter of the hole. This follows from choosing a Gaussian sphere with radius R that goes through the charge layer, showing that the total amount of charge inside the sphere is Q/2 and the E-field inside the hole is 1/2 * Q/ (4R^2 pi * epsilon_0). This applies
  • #1
CsLevi
4
0
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?
 
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  • #2
If the charge is a uniform surface charge, then the field inside would be zero by Gauss's law.
 
  • #3
Even inside the hole when being half outside, half inside the sphere?
 
  • #4
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
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
That happens anywhere at the surface, not just at the hole.
 
  • #7
Interesting, thanks!
 

Related to E-field & hollow non-conducting sphere

1. What is an electric field?

An electric field is a physical quantity that describes the influence of an electric charge on other charges in its vicinity. It is a vector quantity, meaning it has both magnitude and direction.

2. How is an electric field created around a hollow non-conducting sphere?

The electric field around a hollow non-conducting sphere is created by the distribution of charges on its surface. The charges on the surface of the sphere repel each other, creating an electric field that points radially outward from the surface.

3. What is the relationship between the electric field and the surface charge density of a hollow non-conducting sphere?

The electric field inside a hollow non-conducting sphere is directly proportional to the surface charge density. This means that as the surface charge density increases, the electric field also increases.

4. How does the electric field inside a hollow non-conducting sphere vary with distance from the center?

The electric field inside a hollow non-conducting sphere is constant at all points within the sphere. This is because the electric field is created by the surface charges, which are evenly distributed on the surface of the sphere.

5. Can the electric field inside a hollow non-conducting sphere be zero?

Yes, the electric field inside a hollow non-conducting sphere can be zero if there are no charges present on the surface. This can occur if the sphere is completely neutral or if the charges on the surface cancel each other out.

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