Question

Magnetic induction at the center of a circular loop carrying a current is B. If A is the area of the coil, the magnetic dipole moment of the loop is :

• A. $\frac{B{A}^2}{{\mu }_0\pi }$
• B. $\frac{BA\sqrt{A}}{{\mu }_0}$
• C. $\frac{BA\sqrt{A}}{{\mu }_0\pi }$
• D. $\frac{2BA}{{\mu }_0}\sqrt{\frac{A}{\pi }}$

Answer 1

The correct option is D $\frac{2BA}{{\mu }_0}\sqrt{\frac{A}{\pi }}$

Magnetic field at the centre of the coil is,

$B=\frac{{\mu }_{0}i}{2r}$

$A=\pi r^2$

magnetic dipole moment=$i\cdot A$

=$(\frac{2rB}{{\mu }_0})\cdot A$

=$\frac{2B}{{\mu }_0}.A.\sqrt{\frac{A}{\pi }}$