(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Short sections of two very long parallel lines of charge are shown, fixed in place, separated by L = 8.0cm. The uniform linear charge densities are [tex]+6.0\mu[/tex]C/m for line 1 and [tex]-2.0\mu[/tex]C/m for line 2. Where along the x axis shown is the net electric field from the two lines zero?

The known data is:

[tex]\lambda_{1} = 6 \times 10^{-6} C[/tex]

[tex]\lambda_{2} = -2 \times 10^{-6} C[/tex]

[tex]L = 0.08m[/tex]

http://www.clan-dm.net/members/jen/netfield.jpg [Broken]

(sorry, scanner doesn't like big books)

2. Relevant equations

line of infinite charge: [tex]\frac{\lambda}{2\pi \epsilon_{0}r}[/tex]

permittivity constant: [tex]\epsilon_{0} = 8.85*10^{-12}[/tex]

3. The attempt at a solution

I didn't get very far with this one. From what I can tell, I need to sum the electric fields, and figure out when it's zero.

I started out like this:

0 = E1 + E2

E1 = -E2

Obviously, at this point substituting E for the line of infinite charge equation proved fruitless. I don't know if I'm overcomplicating, undercomplicating, or just plain clueless. Any help is appreciated. :)

Also, the given answer makes no sense to me:

[tex]x = \frac{\lambda_{1} - \lambda_{2}}{\lambda_{1} + \lambda_{2}}\left( \frac{L}{2} \right)[/tex]

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# Homework Help: Two lines of charge, net electric field

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