Ok, so here's the question. I've pretty much got it except I'm having trouble with one part of constructing the integral. The problem is...(adsbygoogle = window.adsbygoogle || []).push({});

An insulator which lies between the positions -d[tex]\hat{z}[/tex] and d[tex]\hat{z}[/tex] has a nonuniform linear charge density [tex]\lambda[/tex] = [tex]\lambda_{o}[/tex][tex]\frac{z}{d}[/tex] . Find the force on a charge 'q' located at 3d[tex]\hat{z}[/tex].

2. Relevant equations

[tex]\int[/tex] d[tex]\vec{E}[/tex] = [tex]\int[/tex][tex]\frac{k dq}{r^{2}}[/tex][tex]\hat{z}[/tex]

dq = [tex]\lambda[/tex]dz

[tex]\lambda[/tex] = [tex]\lambda_{o}[/tex][tex]\frac{z}{d}[/tex]

3. The attempt at a solution

What I ended up getting when constructing the integral is...

[tex]\int[/tex][tex]^{ d}_{-d}[/tex]k[tex]\frac{\lambda_{0} z dz}{d r^{2}}[/tex][tex]\hat{z}[/tex]

Now I'm having trouble with the r[tex]^{2}[/tex] part in the denominator...I know it should be something like...

(r [tex]\pm[/tex] something)[tex]^{2}[/tex]

...but I'm just not sure what it is...any help would be greatly appreciated.

Thanks!

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# Homework Help: Electric Force on a charge effected by a non-uniform linear charge

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