b
Magnetic field at the centre of \(\operatorname{loop}, B_{1}=\frac{\mu_{0} I}{2 R}\) 

Dipole moment of circular loop is \(m=I A\) 

\(\mathrm{m}_{1}=\mathrm{I} \cdot \mathrm{A}=\mathrm{I} \pi \mathrm{R}^{2} \quad\{\mathrm{R}=\text { Radius of the loop }\}\)

If moment is doubled (keeping current constant) \(R\) becomes \(\sqrt{2 \mathrm{R}}\)

\({{\text{m}}_2} = {\text{L}}\pi {(\sqrt 2 {\text{R}})^2} = 2.{\text{I}}\pi {{\text{R}}^2} = 2{{\text{m}}_1}\)

\(B_{2}=\frac{\mu_{0} I}{2(\sqrt{2} R)}\)