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Electric Field for an infinite line of charge along the x axis Edit

Consider an infinite line of charge along the x axis with a charge density $ \lambda $. Using Gauss's law, we find at a distance r from the line of charge, the magnitude of the electric field is $ \frac{\lambda}{2\pi\epsilon_{0}} $. The direction is radially away from the line, i.e. proportional to the angle with the y-axis $ \theta $. We have basically just specified the electric field using polar coordinates. We can convert to cartesian coordinates to get:

$ \mathbf{E}(x,y,z) = \frac{\lambda}{2\pi\epsilon_{0}}\left(0,\frac{y}{y^2+z^2},\frac{z}{y^2+z^2}\right) $

(yes, the curl is zero). I used this to solve tutorial 3 extra problem 1.