Question

A magnet of moment $M$, is cut into two equal parts. The two parts are placed perpendicular to each other so that their north poles touch each other. The resultant magnetic moment is :

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

Answer 1

Answer: (B)

$\frac{M}{\sqrt{2}}$

Two parts are placed perpendicular, therefore, $\theta ={90}^o$

After cutting magnet into two equal parts the magnetic moment of each part becomes $M/2$.

Then the resultant magnetic moment is $=M_R=\sqrt{(M/2{)}^2+(M/2{)}^2+2\left(M/2\right)\left(M/2\right)\cos \theta }$

but $cos\theta =cos{90}^o=0$

$M_R=\sqrt{(M/2{)}^2+(M/2{)}^2+0}$

$M_R=\sqrt{\frac{2M^2}{4}}$

$\therefore M_R=\frac{M}{\sqrt{2}}$