Verified 30 May 2026.
A circular loop of radius $R$ carries current $I$. The magnetic field at a point on the axis at distance $x$ from the center is:
$\frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}}$
$\frac{\mu_0 I}{2R}$
$\frac{\mu_0 I R}{2(R^2 + x^2)}$
$\frac{\mu_0 I x^2}{2R^3}$
Using the Biot-Savart law, the axial magnetic field of a circular loop:
$$B = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}}$$
At the center ($x = 0$): $B = \frac{\mu_0 I}{2R}$
At large distance ($x \gg R$): $B \approx \frac{\mu_0 I R^2}{2x^3} = \frac{\mu_0 m}{4\pi x^3}$ (dipole field)
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