- #1

Const@ntine

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## Homework Statement

A charged, straight line/rod of infinite length has a Discrete uniform distribution of charge, has a linear density of λ and is at a distance d from a sphere with a radius of R.

Find the entirety of the Electrical Flux that is caused by this charged rod, which passes through the surface of the sphere.

a) When R < d

b) When R > d

## Homework Equations

[/B]

Φ

_{Ε}= ∫E

^{→}⋅dA

^{→}(for a surface)

Φ

_{Ε}= q

_{internal}/ε

_{0}(Gauss' Law)

E = k

_{e}∫(dq/r

^{2})r

^{∧}(the r here is a Euclidean Vector)

λ = Q/l

## The Attempt at a Solution

a) Okay, so we know that we have an Electrical Flux only when there is a charge inside the sphere/surrounding shape, because otherwise all the lines of the Electric Field go through one point of the shape, and leave through another, resulting in Φ

_{Ε}= 0.

Because R < d, the rod/line is outside the sphere, and thus what we described above happens.

β) Here's where I'm stuck. My initial idea was:

-I'll find E.

-Then I'll use the Φ

_{Ε}= ∫E

^{→}⋅dA

^{→}(for a surface)

Problem is, I'm not sure how to tackle the finding E part. All the exercises I did on that part where with a straight rod on the x axis. Basically I'm having trouble with doing the integration at E = k

_{e}∫dq/r

^{2}r

^{∧}

I'm having a bit of trouble with all the integrals and whatnot here, so I could use a nudge or two. Electrics is entirely new to me so I don't have anywhere to run back to, like with previous semesters.

Any help is appreciated!