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Homework Statement
Find the electric field a distance ##z## above center of a square loop of wire,each of whose sides has length ##l## and uniform charge per length ##λ##
Homework Equations
##dE=\frac {1} {4πε_0} dq \frac {1} {r^2}## (magnitude)
The Attempt at a Solution
I have a pic.
So ##dq=λdx##
##dE=\frac {1} {4πε_0} dq \frac {1} {r^2}##
##r^2## is here
##x^2+(\frac {l^2} {4})+z^2##
##E_x=E_y=0##
so the equation becomes,
##dE=\frac {1} {4πε_0} dq \frac {1} {x^2+(\frac {l^2} {4})+z^2}sinθ## which its
##dE=\frac {1} {4πε_0} dq \frac {1} {x^2+(\frac {l^2} {4})+z^2}\frac {z} {\sqrt {(\frac {l^2} {4})+x^2}}##
From there I get
##E=\frac {zλ} {4πε_0}\int_{\frac {-l} {2}}^{\frac {l} {2}}\frac {8} {(4x^2+l^2+4z^2)(\sqrt {l^2+4z^2})} \, dx##
I stucked at the integral part.I tried calculator but it didnt work out.And before that, are my equations true ? Of course for result I have to mulitply this by ##4## so the answer is
##E_{total}=4E##
It will be in the vertical direction
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