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# Electric Potential WA #12

## Question

Hello,

I got to this question and was not sure how to go about it. I sorta had an idea but that was for the line charge of a fixed length, so do I just ignore the lengths and assume that E= lamda/(4 pi e0) and then use V=int(E*dl)?

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Good strategy, but the electric field due to a line of charge isn't lambda/(4 pi e0).  Use Gauss's law to derive it.  It's in your notes, in the Gauss's Law video, and also in the course guides.

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So I should get (-lamda*r)/(2*pi*e0)+c for the electric potential right?

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Looks like your integration is off a bit...

${V_p} = - \int_{{r_{ref}}}^{{r_p}} {\vec E \bullet d\vec l} = - \int_{{r_{ref}}}^{{r_p}} {{\lambda \over {2\pi {\varepsilon _0}r}}dr = } - {\lambda \over {2\pi {\varepsilon _0}}}\int_{{r_{ref}}}^{{r_p}} {{{dr} \over r} = ...}$   More math here, then:

$V(2m) = - {\lambda \over {2\pi {\varepsilon _0}}}\ln \left( {{{{r_p}} \over {{r_{ref}}}}} \right)$

From there you just substitute in your specific values for the distance from the line and the reference distance (2.5m)

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