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

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Homework Help Overview

The problem involves calculating the electric flux through a hole in a nonconductive hollow sphere surrounding a point charge. The sphere has a radius of 10.0 cm, and the charge is 20.0 µC located at the origin. A hole with a radius of 1.00 mm is drilled along the z-axis.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the method of calculating electric flux by considering the ratio of the areas of the hole and the sphere. Questions are raised about the correct expression for the surface area of the sphere and the implications of using πr².

Discussion Status

Some participants have provided guidance on ensuring the correct area formula is used, while others are clarifying assumptions about the dielectric constant and the thickness of the sphere. There is an ongoing exploration of the implications of the area ratio in the calculations.

Contextual Notes

There are mentions of potential misunderstandings regarding the surface area formula and the need for clarity on the dielectric properties of the sphere, which may not have been provided in the original problem statement.

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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