- #1
bowlbase
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Homework Statement
A wire at extends for -L to L on the z-axis with charge ##\lambda##. Find the field at points on the xy-plane
Homework Equations
##E(r)=k\int\frac{\rho}{r^2}dq##
##k=\frac{1}{4\pi ε_o}##
The Attempt at a Solution
First time I've looked for field on a plane so I wasn't sure if I'm doing this correctly.
##dq=\lambda dz=2L\lambda##
I made a right triangle with one side L and the other two x and y.
##r^2=L^2+x^2+y^2## where only x and y change so I have dxdy.
So, the final integral
##k(2L\lambda)\int\int\frac{1}{L^2+x^2+y^2}dxdy## with limits 0→∞.
I expect at large x,y that the field should be very small and small x,y it should be large. This integral satisfies both of those conditions.
The method I saw our professor do for another, somewhat similar, problem was exceedingly more complicated than this.