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brkomir
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Homework Statement
On a long dielectric line a charge with density ##10^{-3}## is applied one half with positive charge and the other half with negative charge. Perpendicular to the first line and 5 cm away from it we have another line with the same charge density and also half of it is positive while the other half is negative. Points on the line where the charge changes from positive to negative, are the closest. (meaning they are 5 cm apart). Determine the vector of force between the lines.
Homework Equations
The Attempt at a Solution
I hope at least some of the things written below are ok:
Density of charge is ##\rho =e/l## meaning ##de=\rho \frac{dx}{l}##.
Vector from the origin to the point on horizontal line ##\vec r=(x,0,h)## if ##h## is the distance between the lines. Vector from the origin to the point on vertical line is ##\vec r^{'}=(0,y,0)##
So finally
##dF=dedE=\frac{\rho ^2}{l^2}dxdy\frac{1}{4\pi \epsilon _0}\frac{(x,-y,h)}{(x^2+y^2+z^2)^{3/2}}##
But if I integrate this from ##-\infty ## to ##\infty ## the integral does not converge... Did I do anything wrong or is this simply the correct answer? :/