The dipole moment of a circular loop carrying a current $I$, is $m$ and the magnetic field at the centre of the loop is $B_1$ . When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $B_2$ . The ratio $\frac{{{B_1}}}{{{B_2}}}$ is
JEE MAIN 2018, Medium
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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 $\sqrt{2 \mathrm{R}}$
${{\text{m}}_2} = {\text{L}}\pi {(\sqrt 2 {\text{R}})^2} = 2.{\text{I}}\pi {{\text{R}}^2} = 2{{\text{m}}_1}$
$B_{2}=\frac{\mu_{0} I}{2(\sqrt{2} R)}$
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