On the axis of a circular current loop of radius R, at a distance x ≫ R, the magnetic field can be written in terms of the moment m as:
- (μ₀/4π)(2m / x²)
- (μ₀/4π)(m / x³)
- (μ₀/4π)(2m / x³)
- (μ₀/2π)(m / x³)
Show answer and solution
Correct answer: C. (μ₀/4π)(2m / x³)
1. Axial field: $B = \dfrac{\mu_0 I R^2}{2(x^2+R^2)^{3/2}}$.
2. For $x \gg R$, drop $R^2$: $B \approx \dfrac{\mu_0 I R^2}{2x^3}$.
3. Using $m = I\pi R^2$, write $B = \dfrac{\mu_0 m}{2\pi x^3}$.
4. Rearranged: $B = \dfrac{\mu_0}{4\pi}\dfrac{2m}{x^3}$, the axial dipole form.
_Source: syllabus Physics Ch 4 "Moving Charges and Magnetism", p.155_