(a) The net electric field strength at the point O due to straight parts of the thread equals zero. For the curved part (arc) let us derive a general expression i.e. let us calculate the field strength at the centre of arc of radius R and linear charge density λ and which subtends angle θ_{o} at the centre.

From the symmetry the sought field strength will be directed along the bisector of the angle θ_{o} and is given by

In our problem θ_{0} = π/2 thus the field strength due to the turned part at the point which is also the sought result.

(b) Using the solution of 3.14 (a) , net field strength at O due to stright parts equals

and is directed vertically down. Now using the solution of 3.15

(a), field strength due to the given curved part (semi-circle) at the point O becomes and is directed vertically upward. Hence the sought net field strengh becomes zero.