Question

What went wrong?

Answer 1

I'm going to write and draw the problem, give me a min

Answer 2

Sun spots. It's almost always sun spots!

Answer 3

the radius=a
here is what is bothering me. I understand everything up to the point where we change \[\lambda(\theta) \] to \[\lambda\]
ok here we go
\[dE=\frac{kdq}{a^2}=\frac{k\lambda(\theta)}{a^2}ds=\frac{k\lambda(\theta)ad\theta}{a^2}=\frac{k\lambda(\theta)}{a}\]
\[d\vec{E}=-dE_x\hat i-dE_y \hat j\]
then all of a sudden \[\lambda(\theta) \rightarrow \lambda\]
\[d\vec E=-k\lambda\frac{d\theta}acos\theta\hat i -k\lambda \frac{d\theta}asin\theta \hat j\]