Question

Magnetic induction at the centre of a circular loop of area $\pi m^2$ is $0.1T$ . The magnetic moment of the loop is :
( ${\mu }_0$ is permeability of air)

• A. $\frac{0.1\pi }{{\mu }_0}$
• B. $\frac{0.2\pi }{{\mu }_0}$
• C. $\frac{0.3\pi }{{\mu }_0}$
• D. $\frac{0.4\pi }{{\mu }_0}$

Answer 1

Answer: (B)

$\frac{0.2\pi }{{\mu }_0}$

$B$ at centre of loop = $\frac{{\mu }_{0}i}{2r}$
Given area of loop is A = $\pi$ $\Rightarrow r=1m$
$0.1T=$ $\frac{{\mu }_{0}i}{2\times 1}$
$i=$$\frac{0.2}{{\mu }_0}$
Magnetic moment $=i\times A=$ $\frac{0.2}{{\mu }_0}\times A=\frac{0.2\pi }{{\mu }_0}$