Electric Field at Surface & Inside Thin Hollow Sphere

In summary, the conversation is about solving for the magnitude of the electric field at the surface of an insulating, thin, hollow sphere with uniform surface charge density, a. Part a suggests using Gauss' Law or considering the surface of the sphere as flat to solve for the electric field. Part b discusses the addition of a tiny hole in the sphere and the resulting change in the electric field, which can be solved by viewing it as a superposition of the original sphere and the hole. The field of a surface charge is also mentioned as a solution method.
  • #1
PinkFlamingo
19
0
I'm also stuck on this one. Could someone help me please? :confused:

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
 
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  • #2
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.
 
  • #3
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 seperately and then add them up. The field of the sphere you've computed already (zero inside!), and the field of a surface charge is...
 
  • #4
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...
 

What is the difference between electric field at the surface and inside a thin hollow sphere?

The electric field at the surface of a thin hollow sphere is the result of the net charge on the surface, while the electric field inside the sphere is the result of the charge distribution throughout the sphere's interior.

How is the electric field at the surface of a thin hollow sphere calculated?

The electric field at the surface of a thin hollow sphere can be calculated using Coulomb's law, which states that the electric field is equal to the charge divided by the distance squared.

What happens to the electric field at the surface of a thin hollow sphere if the charge distribution inside the sphere changes?

If the charge distribution inside the thin hollow sphere changes, the electric field at the surface will also change. This is because the net charge on the surface will change, resulting in a different electric field.

Can the electric field at the surface of a thin hollow sphere be zero?

Yes, the electric field at the surface of a thin hollow sphere can be zero if the net charge on the surface is zero. This means that the charge distribution inside the sphere is such that the electric field vectors cancel out at the surface.

How does the electric field at the surface of a thin hollow sphere affect objects placed near it?

The electric field at the surface of a thin hollow sphere can affect nearby objects by exerting a force on them. This force is dependent on the charge and distance of the objects from the surface of the sphere.

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