Select the correct option based on the statements:
Statement I: The magnetic field of a circular loop at very

Question

Select the correct option based on the statements:
Statement I: The magnetic field of a circular loop at very far away point on the axial line varies with distance as like that of a magnetic dipole.
Statement II: The magnetic field due to magnetic dipole varies inversely with the square of the distance from the centre on the axial line.

Accepted Answer

1. **Statement I Analysis:** The magnetic field $B$ on the axis of a circular current loop of radius $R$ at a distance $x$ from the centre (where $x \gg R$) is given by the approximation: 
   $$ B \approx \frac{\mu_0 I R^2}{2x^3} $$
   Substituting the magnetic moment $m = I(\pi R^2)$, we get:
   $$ B \approx \frac{\mu_0 m}{2\pi x^3} $$
   This shows the field varies as $1/x^3$, which is the characteristic behavior of a magnetic dipole. Thus, Statement I is **correct**.
2. **Statement II Analysis:** The magnetic field due to a magnetic dipole (or bar magnet) on the axial line at distance $r$ is given by:
   $$ B_{	ext{axial}} = \frac{\mu_0}{4\pi} \frac{2m}{r^3} $$
   This indicates that the field varies inversely with the **cube** of the distance ($1/r^3$), not the square ($1/r^2$). Inverse square dependence applies to electric monopoles (point charges), not dipoles. Thus, Statement II is **incorrect**.

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