The ratio of magnetic field at the centre of a circular current carrying coil to its magnetic moment is ${}^{\text{'}}X^{\text{'}}$. If the current in the wire is doubled, the ratio will become (radius is constant)

Given data:

ratio of magnetic field is x

Concept used: magnetic dipole moment

Detailed solution:

At the center, current carrying coil’s magnetic field is  $\mathrm{B}=\frac{{\mu }_0\mathrm{i}}{2\mathrm{r}}$

Magnetic moment is $\mathrm{M}=\mathrm{i}\pi {\mathrm{r}}^2$

Given ratio is

$\mathrm{x}=\frac{\mathrm{B}}{\mathrm{M}}$

$\mathrm{x}=\frac{{\mu }_0}{2\pi {\mathrm{r}}^3}$

Upon doubling the current, the ratio will not change.