The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of $20 \mathrm{cm}$ from its center is $1.5\times {10}^{-5} \mathrm{T} \mathrm{m}$. The magnetic moment of the dipole is _______ $\mathrm{A} {\mathrm{m}}^2$. (Given : $\frac{{\mu }_0}{4\pi }={10}^{-7 }\mathrm{T} \mathrm{m} {\mathrm{A}}^{-1}$)

The formula to calculate the magnetic potential due to a magnetic dipole can be written as

$V=\frac{{\mu }_0}{4\pi }\frac{M}{r^2} ...\left(1\right)$

Substitute the values of the known parameters into equation (1) and solve to calculate the required magnetic moment of the dipole.

$$\begin{gathered} 1.5\times {10}^{-5}={10}^{-7}\times \frac{M}{{\left(20\times {10}^{-2}\right)}^2} \\ \Rightarrow M=\frac{1.5\times {10}^{-5}\times 20\times 20\times {10}^{-4}}{{10}^{-7}} \\ \Rightarrow M=1.5\times 4=6 \mathrm{A} {\mathrm{m}}^2 \end{gathered}$$