An infinite straight current carrying conductor is bent in such a way that a circular loop is formed on it as shown in figure. If the radius of the loop is \(R\) the magnetic field at the centre of the loop is _______.

D
Magnetic field at the center due to the wire
\(B_{\text {wire }}=\frac{\mu_0 I}{2 \pi R}=\frac{2 \mu_0 I}{4 \pi R}\) (inside)
Magnetic field at the center due to the loop
\(\begin{aligned} B_{\text {loop }}=\frac{\mu_0 I}{2 R} =\frac{\mu_0 I}{2 R} \times \frac{2 \pi}{2 \pi} \\ =\frac{\mu_0}{4 \pi} \cdot \frac{2 \pi I}{R} \text { (inside) }\end{aligned}\)
Since both magnetic field are in same direction net magnetic field.
\(\begin{aligned} B=B_{\text {wire }}+B_{\text {loop }} \\ \therefore B=\frac{2 \mu_0 I}{4 \pi R}+\frac{2 \mu_0 I \pi}{4 \pi R} \\ \therefore B=\frac{\mu_0}{4 \pi} \frac{2 I}{R}(\pi+1) \text { (inside) }\end{aligned}\)