Homework Help: Find the Electric Flux Through a Hole In a Sphere

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SUMMARY

The discussion focuses on calculating the electric flux through a drilled hole in a nonconductive hollow sphere surrounding a 20.0 µC charge. The correct approach involves using the formula for electric flux, Φ = Q/ε0, and applying the ratio of the areas of the hole to the sphere. Participants emphasized the importance of using the correct surface area formula for the sphere, which is 4πr², rather than πr². The solution requires careful attention to the geometry involved in the problem.

PREREQUISITES
  • Understanding of electric flux and Gauss's Law
  • Familiarity with the concept of surface area of a sphere
  • Knowledge of the dielectric constant in nonconductive materials
  • Basic algebra for manipulating equations
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  • Study the surface area calculations for different geometric shapes
  • Explore the implications of dielectric constants in electric fields
  • Practice problems involving electric flux in various configurations
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Pratik007789
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Homework Statement


[/B]
An uncharged nonconductive hollow sphere of radius 10.0 cm surrounds a 20.0 µC charge located at the origin of a cartesian coordinate system. A drill with a radius of 1.00 mm is aligned along the z axis, and a hole is drilled in the sphere. Calculate the electric flux through the hole.

Homework Equations


[/B]
Volume charge distribution = Q/V
Flux = q/ε0 = EA

The Attempt at a Solution


In the picture
But the answer is coming out to be wrong
 

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Could you please try to Upload your work again so that it is not sideways? Thanks.

Also, I didn't look at your work yet (since it was sideways), but are the dielectric constant and the thickness of the non-conducting sphere given?
 
I looked at your work and I was able to read it because I have a laptop that I can rotate 90o. Your method is correct, you multiply the total flux Q/ε0 by the ratio of the areas of hole to sphere. The only problem is that the area of the sphere is not πr2. If you use the correct expression for the area, you will be OK.
 
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kuruman said:
I looked at your work and I was able to read it because I have a laptop that I can rotate 90o. Your method is correct, you multiply the total flux Q/ε0 by the ratio of the areas of hole to sphere. The only problem is that the area of the sphere is not πr2. If you use the correct expression for the area, you will be OK.
But If I we have to ratio at the end then the other terms like 2, π won't cancel out? Any support would be appreciated
 
Pratik007789 said:
But If I we have to ratio at the end then the other terms like 2, π won't cancel out? Any support would be appreciated
Not sure what you mean, but I feel you have not understood kuruman's response. What is the surface area of a sphere radius r? Use that instead of the πr2 that you used.
 
haruspex said:
What is the surface area of a sphere radius r? Use that instead of the πr2 that you used.
Yes, do that and if something cancels out, so be it. You will have a simpler expression to deal with.
 
Thanks guys. Really appreciate your help and support.
 

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