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 $m =I A )$ is

• A. $B =\frac{\mu_{0} m }{x^{3}}$
• B. $B =\frac{\mu_{0}}{4 \pi} \frac{ m }{x^{3}}$
• C. $B =\frac{\mu_{0}}{4 \pi} \frac{2 m }{x^{3}}$
• 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}{2 x^{3}} $
$\Rightarrow B=\frac{\mu_{0} I A}{2 \pi x^{3}}$
Hence, $B \simeq \frac{\mu_{0} m }{2 \pi x^{3}}=\frac{\mu_{0}}{4 \pi} \times \frac{2 m }{x^{3}}$