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

AI Thread Summary
An uncharged nonconductive hollow sphere surrounds a 20.0 µC charge, and the task is to calculate the electric flux through a drilled hole. The correct approach involves using the total flux formula Q/ε0 and adjusting it by the ratio of the areas of the hole to the sphere. A key point of confusion was the incorrect use of the area formula for the sphere, which should not be πr². Clarification emphasized that using the correct surface area formula is crucial for accurate calculations. Overall, understanding the area relationship is essential for solving the problem correctly.
Pratik007789
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Homework Statement


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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


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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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