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Const@ntine

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## Homework Statement

An uncharged, unconductive, hollow sphere with a radius R of 10.0 cm, surrounds an electric charge of 10.0 μC, which is found at the beginning of the axises, in a standard cartesian system.

Parallel to the z axis, a small drill with a radius r = 1.00 mm opens a hole in the sphere.

What's the Electric Flux that goes through that opening?

## Homework Equations

Φ

_{Ε}= ∫E

^{→}⋅dA

^{→}(for a surface)

Φ

_{Ε}= q

_{internal}/ε

_{0}(Gauss' Law)

## The Attempt at a Solution

I'm honestly pretty lost here. The book doesn't offer any examples, and only has a small paragraph on this part. From what I'm getting, I need to find the EF on that single part, so I cannot use the Law, since it refers to a whole area that surrounds the charge.

At first, I figured that since the charge is in the beginning of the axises, then its distance from the opening would be: d = R - 2r = 0.098 m

Problem is, I get stuck there because I'm not exactly sure how the whole thing works yet. The integration for example. The book says that E is always constant on the surface. Because its vector is parallel to the surfaces, the angle between them is 0. And so you have only dA to integrate, which results in just the A. I tried doing that computation (E*A) but I don't get the correct result.

Any help untangling this so that I can understand the basics would be appreciated!

PS: The book's answer is Φ

_{Ε}= 28.2 Nm

^{2}/C