Question

If a bar magnet of pole strength m and magnetic moment M is cut equally $5$ times parallel to its axis and again $3$ times perpendicular to its axis, then the pole strength and magnetic moment of each piece are respectively:

• A. $\frac{m}{20},\frac{M}{4}$
• B. $\frac{m}{5},\frac{M}{20}$
• C. $\frac{m}{6},\frac{M}{24}$
• D. $\frac{m}{5},\frac{M}{24}$

Answer 1

Answer: (C)

$\frac{m}{6},\frac{M}{24}$

Pole strength $=m$

Magnetic moment $=M=m\times 2L$

When it is cut five times parallel to its axis:

Pole strength, $m^{\prime }=\frac{m}{6}$

When it is cut three time perpendicular to its axis, then length $2L^{\prime }=\frac{2L}{4}$

So, Pole strength, $m^{\prime }=\frac{m}{6}$

And, Magnetic moment, $M^{\prime }=\left(\frac{m}{6}\right)\left(\frac{2L}{4}\right)=\frac{M}{24}$