a
\(\therefore B(\) at \(P)=\frac{\mu_{0} I}{4 \pi d}\left(\cos \theta_{1}-\cos \theta_{2}\right)\)

In given case,

\(d=R \sin 45^{\circ}=\frac{R}{\sqrt{2}}\)

\(\theta_{1}=135^{\circ}, \theta_{2}=180^{\circ}\)

\(\therefore B(\) at \(P)=\frac{\mu_{0} I}{4 \pi\left(\frac{R}{\sqrt{2}}\right)}\left[\cos 135^{\circ}-\cos 180^{\circ}\right]\)

\(=\frac{\mu_{0} I}{4 \pi R} \sqrt{2}\left(\frac{-1}{\sqrt{2}}-(-1)\right)\)

\(=\frac{\mu_{0} I}{4 \pi R} \sqrt{2}\left(\frac{\sqrt{2}-1}{\sqrt{2}}\right)\)

or \(B(\) at \(P)=\frac{\mu_{\rho} I}{4 \pi R}(\sqrt{2}-1) T\)