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

A non-uniformly charged semicircle of radius R=28.0 cm lies in the xy plane, centered at the origin, as shown. The charge density varies as the angle θ (in radians) according to λ = + 5.8 θ, where λ has units of μC/m.

(picture included)

What is the y - component of the electric field at the origin?

2. Relevant equations

dE=[tex]\frac{dq}{4\pi\epsilon r^{2}}sin\theta[/tex]

where [tex]\epsilon[/tex] = 8.85*10^{-12}

[tex]\theta r = s[/tex]

[tex]\lambda=\frac{q}{s}[/tex]

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3. The attempt at a solution

First I derived [tex](5.8*10^{-6})\theta^{2} r=q[/tex]

and took the derivative [tex]2(5.8*10^{-6}) r \theta d\theta=dq[/tex]

substituted into equation 1

dE=[tex]\frac{2(5.8*10^{-6})}{4\pi\epsilon r}\theta sin(\theta)d\theta[/tex]

Integrated from 0 to pi.

E=[tex]\frac{(5.8*10^{-6})}{2\pi\epsilon r}\int\theta sin(\theta)d\theta[/tex]

The whole integral simplifies down to pi,which cancels out and leaves

E=[tex]\frac{(5.8*10^{-6})}{2\epsilon r}[/tex]

I am getting 1.17*10^{6} N/C for an answer, but it's not correct.

Thanks for the help in advance.

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# Homework Help: Nonuniform Semicircle of Charge problem

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