Question

The dipole moment of a circular loop carrying a current $I$, is $m$ and the magnetic field at the centre of the loop is $B_1$. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $B_2$. The ratio $\frac{B_1}{B_2}$ is :

• A. $2$
• B. $\sqrt{3}$
• C. $\sqrt{2}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

Answer: (C)

$\sqrt{2}$

Answer 2

$m=I\left(\pi R^{2}\right), \,\,\, m'=2 m=I \times(\pi \sqrt{2} R)^{2}$ $\therefore R'=\sqrt{2} R$ $B_{1}=\frac{\mu_{0} I}{2 R}$ $B_{2}=\frac{\mu_{0} I}{2 \times(\sqrt{2} R)}$ $\therefore \frac{B_{1}}{B_{2}}=\sqrt{2}$