Question

A bar magnet is 0.10m long and its pole strength is 120Am. Find the magnitude of magnetic field at a point on the its axis at a distance 20cm from it.

Answer 1

Hint: Here the length of the magnet and pole strength are given, hence calculate the magnetic moment of the bar magnet. The magnetic moment is twice the product of its pole strength and the half length of the magnet. Then by applying the equation for the magnetic field calculate the magnetic field on the axial line.

Formula used: $B=\dfrac{{{\mu }_{0}}}{4\pi }\dfrac{2md}{{{\left( {{d}^{2}}-{{l}^{2}} \right)}^{2}}}$
where, B is the magnetic field
${{\mu }_{0}}$ is the permeability of free space
m is the magnetic moment
d is the distance from the axis
l - half length of the bar magnet.

Complete step by step answer:

Length of a bar magnet,
$2l=0.1m$
$\Rightarrow l=\dfrac{0.1}{2}=0.05m$
Given that pole strength $=120Am$
Thus magnetic moment is,
$\begin{align}
  & m=2Ml=2\times 120\times 0.05 \\
 & \Rightarrow m=12A{{m}^{2}} \\
\end{align}$
Magnetic field on the axial line is,
$B=\dfrac{{{\mu }_{0}}}{4\pi }\dfrac{2md}{{{\left( {{d}^{2}}-{{l}^{2}} \right)}^{2}}}$
Substituting the values we get,
$B=\dfrac{4\pi \times {{10}^{-7}}}{4\pi }\dfrac{2\times 12\times 0.2}{{{\left( {{\left( 0.2 \right)}^{2}}-{{\left( 0.05 \right)}^{2}} \right)}^{2}}}$
$\Rightarrow B=\dfrac{4.8\times {{10}^{-7}}}{1.406\times {{10}^{-3}}}$
$\therefore B=3.42\times {{10}^{-4}}T$

Thus, the magnitude of magnetic field at a point on the its axis at a distance 20cm is $3.42\times {{10}^{-4}}T$ .

Additional Information: The magnetic phenomena are universal in nature. The earth behaves as a magnetic field pointing in geographic south to north. When a bar magnet is freely suspended, it points in the north- south direction. The tip which points to geographic north is called north pole and the tip which points to the geographic south is called the south pole of the magnet. There will be a repulsive force when north poles of two magnets are brought close together. We cannot isolate the north, or south poles of a magnet. That is, if we broke a bar magnet into two halves, we get two bar magnets of similar but weak properties.

Note: The magnetic phenomena are universal in nature. The pole strength and magnetic moment of a bar magnet are two different properties of a bar magnet. The pole strength has an SI unit $Am$, whereas the unit of magnetic moment is $A{{m}^{2}}$. That is, the magnetic moment is twice the product of its pole strength and the half length of the magnet.