Question

If a bar magnet of pole strength $m$ and magnetic moment $M$ is cut equally into $6$ parts parallel to its axis and again $5$ equal parts perpendicular to its axis, then the pole strength and magnetic moment of each piece respectively:

• A. $m,\frac{M}{6}$
• B. $6m,\frac{M}{5}$
• C. $\frac{m}{6},\frac{M}{5}$
• D. $\frac{m}{6},\frac{M}{30}$

Answer 1

The correct option is D $\frac{m}{6},\frac{M}{30}$

Given,
Pole strength $=m$
Magnetic moment, $M=m\left(2l\right)$
Magnetic length $=2l$

When it is cut into six equal parts parallel to its axis, its pole strength becomes $\frac{m}{6}$.

$\Rightarrow m^{\prime }=\frac{m}{6}$

When it is cut into five equal parts perpendicular to its axis, its length becomes $\frac{L}{5}$

$\Rightarrow L^{\prime }=\frac{L}{5}=\frac{2l}{5}$

Its new magnetic moment becomes,

$M^{\prime }=m{}^{\prime }\times L{}^{\prime }=\left(\frac{m}{6}\right)\left(\frac{2l}{5}\right)=\frac{M}{30}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.

Why this question? When a bar magnet of length $L$ and pole strength $m$ is cut into parallel and perpendicular to its length its magnetic moment varies. When a bar magnet is cut along its length into $n$ equal parts: its length remains the same, but its pole strength becomes $\frac{m}{n}$. When a bar magnet is cut $\perp$ to its length into $n$ equal parts, Its pole strength remains the same but its length becomes $\frac{L}{n}$