here is a question:

http://i25.tinypic.com/8xlcfl.gif

there is endless wire uniformly charged $\displaystyle \lambda=2*10^{-4}C/m$

and close to it located a wire with $\displaystyle l=0.12_m$

which has 30 degree angle between him and the endless wire,and it charged in uniformed way so that the total charge on it is $\displaystyle q=3*10^{-9}$

the distance of the finite wire and the infinite wire is 0.08 meters

A.find the total force acted on the finite wire.

B.find it when $\displaystyle \alpha=0 $degrees and when $\displaystyle \alpha=90 $degrees.

gaus law for infinite wire i presume its length is l and distance r.

$\displaystyle E2\pi r h=\frac{q}{\epsilon_0}\\$

$\displaystyle E=\frac{q}{\epsilon_0 2\pi r h}=\frac{\lambda h}{\epsilon_0 2\pi r h}=\frac{\lambda }{\epsilon_0 2\pi r }\\$

$\displaystyle \frac{q_2}{l_2}=\lambda_2\\$

$\displaystyle l_0=l_2\cos \alpha\\$

$\displaystyle \int_{0}^{l_0}Edl=\int_{0}^{l_0}\frac{\lambda }{\epsilon_0 2\pi r }dl$

i sum along the finite wire

but the ditance from the infinite changes too.

so it should be a double integral

but its not a 2d body

??