Magnetic Dipole And Axial Field

A small current loop is equivalent to a magnetic dipole of moment $m=NIA$, and far along its axis the field mirrors that of a bar magnet: $B_{\text{axial}}=\frac{{\mu }_0}{4\pi }\frac{2m}{r^3}$. This axial field is twice the equatorial field at the same distance, a hallmark of dipole behaviour. Substituting $\frac{{\mu }_0}{4\pi }=10^{-7}$, $m=0.6{\text{A m}}^2$ and $r=0.2\text{m}$ so $r^3=8\times 10^{-3}$, we get $B=10^{-7}\times \frac{2(0.6)}{8\times 10^{-3}}=10^{-7}\times 150=1.5\times 10^{-5}\text{T}$. The option $0.75\times 10^{-5}\text{T}$ is the equatorial field, missing the factor of two. The option $3.0\times 10^{-5}\text{T}$ doubles the moment. The option $6.0\times 10^{-5}\text{T}$ uses $r^2$ instead of $r^3$. NCERT explicitly establishes this analogy between a current loop and a magnetic dipole. A check confirms the inverse-cube falloff and the $10^{-5}\text{T}$ scale at $20\text{cm}$. This equivalence between a current loop and a magnetic dipole is one of the most unifying ideas in magnetism, letting the same mathematics describe a tiny coil, a bar magnet, and even an orbiting atomic electron. The factor-of-two relationship between axial and equatorial fields exactly parallels the electric dipole, reinforcing the deep structural similarity between electrostatic and magnetostatic dipole fields that students should carry forward into later chapters. This same dipole field also governs how a compass needle or a small magnet orients itself and oscillates when suspended in an external magnetic field.