An infinitely long cylindrical surface density `sigma = sigma_(0) cos varphi`. Where `varphi` is the polar angle of the cylindrical coordinate system whose `z` axis coincides with the axis of the given surface. Find the magnitude and direction of the electric field strength vector on the `z` axis.

Answer

`[E-1//2" "sigma_(0)//epsi_(0)`, with the direction of the vector E corresponding to the angle `phi=pi`]