Question

Two short bar magnets of moments $M_1$ and $M_2$ are placed one on the other as shown in the figure. The resultant magnetic induction R at the point P is making 30${}^0$ as shown in the figure. The ratio of the magnetic moments of the magnets is:

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

Answer 1

The correct option is B $\sqrt{3}:2$

$B_1=\frac{2{\mu }_0{m}_1}{4\pi d^3}$
$B_2=\frac{-{\mu }_0{m}_2}{4\pi d^3}$

$\tan {30}^{\circ }=|\frac{B_2}{B_1}|$
$\frac{1}{\sqrt{3}}=\frac{m_2}{2m_1}$
$m_1:m_2=\sqrt{3}:2$