[Gauss' Law] Hollow insulating sphere?

In summary, the problem involves a hollow insulating sphere with a uniform charge density and the question is how to use Gauss' Law to find the electric field at a specific radius. The solution involves using the formula RHO = Q/V and finding the volume enclosed by the given radius. The correct volume to use is (4/3)(pi)(.1170^3 - .0658^3).
  • #1
GeorgeCostanz
31
0

Homework Statement



A hollow insulating sphere with an inner radius of 6.58 cm and outer radius of 11.7 cm has a uniform charge density of 79.9 μC/m3 distributed throughout the volume between.

If we want to use Gauss' Law to find the electric field at r = 17.2 cm, what "charge enclosed" should we use?

Homework Equations



RHO = Q/V

a = .0658 m
b = .1170 m
r = .1720 m

therefore r > b > a

The Attempt at a Solution



i kno RHO = Q/V

i just don't kno what V to use

i've used v = 4/3(pi)(.1720^3)

i've used v = (4/3)(pi)(.1720^3 - .1170^3)

think I've used every combination of r

i kno I'm overlooking something incredibly simple
blah!
 
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  • #2
The charge is only in the middle region and the entire charge is enclosed in a sphere of radius r.

ie,v = (4/3)(pi)(.1170^3 - .0658^3)
 
  • #3
yes that makes perfect sense
and i could have swore i used those r's for v

thanks humanist
 

1. What is Gauss' Law in relation to a hollow insulating sphere?

Gauss' Law states that the electric field passing through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space. In the case of a hollow insulating sphere, the electric field inside the sphere is zero, and the total charge enclosed by the surface is also zero, resulting in an electric field of zero outside the sphere.

2. How does the electric field vary inside a hollow insulating sphere?

The electric field inside a hollow insulating sphere is zero. This is because the electric charges on the inner surface of the sphere create an equal and opposite electric field that cancels out the electric field from the charges on the outer surface.

3. What is the significance of the electric field being zero inside a hollow insulating sphere?

The electric field being zero inside a hollow insulating sphere means that there is no net flow of electric charge within the sphere. This is due to the fact that the electric charges on the inner surface of the sphere are evenly distributed, resulting in a canceling out of the electric field from the outer surface charges.

4. Can Gauss' Law be applied to a hollow insulating sphere with a non-uniform charge distribution?

Yes, Gauss' Law can still be applied to a hollow insulating sphere with a non-uniform charge distribution. The law states that the electric field is directly proportional to the charge enclosed, regardless of the distribution of the charges.

5. How is Gauss' Law used in practical applications involving hollow insulating spheres?

Gauss' Law can be used to calculate the electric field and potential inside and outside of a hollow insulating sphere. This is useful in designing and analyzing devices such as capacitors, where a hollow insulating sphere may be used as one of the conductive plates. It can also be used to calculate the electric field and potential in medical imaging techniques such as MRI, which use hollow insulating spheres to generate and manipulate electric fields.

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