Question

A bar magnet of length 10cm and having pole strength equal to ${{10}^{-1}}Wb$ is kept in a magnetic field. Then, the magnetic moment of the magnet is
A. $\dfrac{10}{{{\mu }_{0}}}$
B. $\dfrac{{{10}^{-4}}}{{{\mu }_{0}}}$
C. $\dfrac{{{\mu }_{0}}}{10}$
D. $\dfrac{{{\mu }_{0}}}{{{10}^{-4}}}$

Answer 1

Hint: A bar magnet has two poles: north and south. It is similar to a dipole. The length and pole strength are given, we shall substitute the given values in the magnetic dipole moment formula. Which is expressed as $M=m\times 2l$

Complete step by step answer:
Magnetic moment is the ability of the magnet to get arranged through a magnetic field. It can also be described as the strength and orientation of a magnet that produces magnetic fields. Some of the objects that possess magnetic moments are permanent magnets, loops of electric current and different molecules. Magnetic moment is a vector quantity which relates the torque of an object to its magnetic field. It can be expressed as,
$\tau =m\times B$
Where, τ is torque
m is the magnetic moment and
B is the magnetic field.
A magnetic dipole has two unlike poles of same strength and separated by a small distance. A bar magnet is a magnetic dipole. The magnetic dipole moment can be described as the product of pole strength and the distance between the poles. The distance between the poles is named a s magnet length and given as 2l. The expression for magnetic dipole can be written as,
$M=m\times 2l$
Where, ‘m’ is the magnetic moment and
‘2l’ is the magnet length
The given pole strength of the magnet, $m=\dfrac{{{10}^{-3}}}{{{\mu }_{0}}}$ and pole strength, $2l=10cm=0.1m$
$M=\dfrac{{{10}^{-3}}}{{{\mu }_{0}}}\times 0.1$
$M=\dfrac{{{10}^{-4}}}{{{\mu }_{0}}}$
Therefore, the correct answer for the given question is option (B).

Note: The unit for magnetic moment is $Amp-{{m}^{2}}$. It can also be written in terms of joules and tesla as $J{{T}^{-1}}$. The two units are equivalent to each other and are provided as $1Amp-{{m}^{-2}}=1J{{T}^{-1}}$.