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jendead
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Homework Statement
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
(sorry, scanner doesn't like big books)
Homework Equations
line of infinite charge: [tex]\frac{\lambda}{2\pi \epsilon_{0}r}[/tex]
permittivity constant: [tex]\epsilon_{0} = 8.85*10^{-12}[/tex]
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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