Question

For a circular current loop magnitude of magnetic field on axis of loop at a point distant $x$ from centre of loop $(x>>R$ and magnetic dipole moment of loop is $m=IA)$ is

• A. $B=\frac{{\mu }_{0}m}{x^3}$
• B. $B=\frac{{\mu }_0}{4\pi }\frac{m}{x^3}$
• C. $B=\frac{{\mu }_0}{4\pi }\frac{2m}{x^3}$
• D. $B=\frac{{\mu }_{0}m\cdot R}{2\pi x^3}$

Answer 1

Answer: (C)

For a loop at a point on its axis distant $x$ from centre,
$B=\frac{{\mu }_{0}I{R}^2}{2{\left(x^2+R^2\right)}^{3/2}}$
For $x>>R,B=\frac{{\mu }_0{R}^{2}I}{2x^3}$
$\Rightarrow B=\frac{{\mu }_{0}IA}{2\pi x^3}$
Hence, $B\simeq \frac{{\mu }_{0}m}{2\pi x^3}=\frac{{\mu }_0}{4\pi }\times \frac{2m}{x^3}$