A wire is bent so that its curved part has a radius a and the two straight parts are at 90, as the figure indicates. If the linear load density of the wire is ?, and choosing a coordinate system such that its axes rest on the straight parts of the wire, prove that the electric field at the center of the curvature O is E = ? / 4??oa (?? + ??)where ?? is the unit vector to the right and ?? upwards.

a) (2 points) Calculate the electric field at the point O produced by the vertical straight part.

b) (0.5 points) Find the electric field at point O produced by the horizontal straight part. Do not repeat the calculation, use the above result, adjusting what is required.

c) (1 point) Calculate the electric field at the point O produced by the curved part.