Consider an infinite line of charge along the x axis with a charge density . Using Gauss's law, we find at a distance r from the line of charge, the magnitude of the electric field is . The direction is radially away from the line, i.e. proportional to the angle with the y-axis . We have basically just specified the electric field using polar coordinates. We can convert to cartesian coordinates to get: (yes, the curl is zero). I used this to solve tutorial 3 extra problem 1.