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

The situation is the one of a hairpin such as in this website : http://www.physics.brocku.ca/Courses/1P22_Crandles/problems/hairpin.jpg.

I must prove that the electric field in "a" is worth 0. There's a tip. It says to calculate the electric field due to a differential part on the semi circle and to compare it with a differential part on the infinite length wire. With both the same angle [tex]\theta[/tex], where theta is the angle between the point over the semicircle considered, point "a" and the vertical radius (bottom one) of the semicircle.

2. Relevant equations

Radius of the semicircle =b.

Linear charge density of the wire : [tex]\lambda[/tex].

3. The attempt at a solution

[tex]d\vec E=\frac{dQ \hat r}{r^2}[/tex]. For the differential portion over the semicircle, I get that [tex]dE=\frac{\lambda \cos (\theta ) d\theta}{b}[/tex]. Obviously I should find the same result for the dE of the differential portion of the straight wire, but I find [tex]\frac{\lambda \left [ \tan (\theta +d\theta) - \tan \theta \right ] }{b \cos ^2 (\theta + d \theta)}[/tex]. I don't think they are the same. At least I've tried to equate them, but with no success.

Did I do everything wrong?

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# Homework Help: Trouble calculating the electric field at a point

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