c
As, \(R\) be the radius of the ring. Consider a small strip of length \(d l\) having charge \(d q\) lying at an angle \(\theta\).

\(d l=R d \theta\)

Charge on \(d l=\lambda R d \theta\)

Force at \(1 C\) due to \(d l\)

\(=\frac{k \lambda R d \theta}{R^{2}}=\frac{k \lambda}{R} d \theta=d F\)

We need to consider only the component \(d F \cos \theta,\) as the component \(d F \sin \theta\) will cancel out because of the symmetrical element \(d l\).

The total force on \(1 C\) is

\(F=\int_{-\pi / 2}^{\pi / 2} d F \cos \theta\)

\(=\frac{k \lambda}{R} \int_{-\pi / 2}^{\pi / 2} \cos \theta d \theta\)

\(=\frac{k \lambda}{R} \times 2=\frac{2 k \lambda}{R}\)