I have a circular arc of wire centered at the point (0,0). It has a radius of [tex]r[/tex], extends from [tex]\theta = -60[/tex] to [tex]\theta = 60[/tex] and also holds a charge [tex]q[/tex]. For the differential electric field I have the following equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

dE = \frac{\lambda ds}{4 \pi \epsilon_0 r^2}

[/tex]

Where [tex]ds[/tex] is the length of a differential element of the arc.

To the find the [tex]x[/tex] component of the electric field I this equation:

[tex]

dE_{x} = \frac{\lambda}{4 \pi \epsilon_0 r^2} cos(\theta)} ds

[/tex]

To integrate this I have to set [tex]ds = r d\theta[/tex] so that the above equation reads:

[tex]

dE_{x} = \frac{\lambda}{4 \pi \epsilon_0 r^2} cos(\theta)} r d\theta

[/tex]

Where does the [tex]r[/tex] come from in the statement [tex]ds = r d\theta[/tex]?

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# Homework Help: Circular arc of charge, integration question

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