A thin nonconducting ring of radius `R` has a linear charge density `lambda = lambda_(0) cos varphi`, where `lambda_(0)` is a constant , `phi` is the azimutahl angle. Find the magnitude of the electric field strength
(a) at the centre of the ring ,
(b) on the axis of the ring as a function of the distance `x` from its centre. Investegation the obtained function at `x gt gt R`.

Answer

(a) `lambda/(4 epsi_(0) R)` (b) `E=(lambda_(0) R^(2))/(4 epsi_(0) (x^(2)+R^(2))^(3//2))`. For `x gt gt R` this strength `E~~ p/(4pi epsi_(0) x^(3))`, where `p=pi R^(2) lambda_(0)`.