Question

A long magnetic needle of length $2l$, magnetic moment $M$ and pole strength $m$ units is broken into two pieces in the middle. The magnetic moment and pole strength of each piece will be:
A. $\dfrac{M}{2},\dfrac{m}{2}$
B. $M,\dfrac{m}{2}$
C. $\dfrac{M}{2},m$
D. $M,m$

Answer 1

To solve this question, we must know about magnetic moment, we know that the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field and using formula we can easily get the answer.

Formula used:
If $m$ is the power of any magnetic pole, then the magnetic dipole moment of the magnet is signified by the vector $M$ and it is represented as
$M = \dfrac{m}{{2l}}$

Complete step by step answer:
Given that, Length $l = 2L$.
${\text{Pole Strength}} = m$
Now, the magnetic moment is
$M = ml$
Now, if cut perpendicular to the axis of magnetic needle
New length $l' = L$
New ${\text{Pole Strength }}m' = m$
Now, new magnetic moment is
$M' = \dfrac{{mL}}{2} \\\ \Rightarrow M'= \dfrac{M}{2}$
Hence, the magnetic moment of each part is $\dfrac{M}{2}$ and the pole strength of each part is $m$.

Therefore, the correct option is C.

Note: A Magnetic Dipole comprises two unlike poles of equivalent strength and parted by a small distance.For instance: The needle of a compass, a bar magnet, etc. are magnetic dipoles. We shall show that a current loop works as a magnetic dipole. Magnetic Dipole Moment is described as the product of pole strength and the distance amidst the two poles. The distance between the two poles of a magnet or a magnetic dipole is named as the magnet length and is given as the $2L$.