Question

The magnetic dipole of a bar magnet of geometric length \[18\,cm\] and pole strength \[100\,Am\] is:
A. \[15\,A{m^2}\]
B. \[18\,A{m^2}\]
C. \[9\,A {m^2}\]
D. \[7.5\,A{m^2}\]

Answer 1

Hint:The magnetic length is always less than the geometric length. The Magnetic length is the distance between the two poles of the magnet. and the geometric length is the actual length of the magnet. When the poles are stronger than the magnetic poles are not exactly at the ends but somewhere near the ends. The magnetic length is the 5/6 times of the geometric length.

Complete step by step solution:
Given values:
The pole strength is, \[m = 100{\text{ }}Am\]
The geometric length is \[18cm\]
The magnetic dipole of a bar magnet is defined as the product of the pole strength and length of the magnet
Magnetic dipole \[ = m \times 2l\]
Where, Length of the bar magnet is \[2l\], the pole strength is $m$

To find out the length of the bar magnet
We know that,
The Length of the bar magnet is 5/6 times of the geometric length
Length of the bar magnet \[ = \dfrac{5}{6} \times geometric{\text{ }}length\]
Length of the bar magnet \[ = \dfrac{5}{6} \times 18 = 15cm = 0.15m\]

To find out the magnetic dipole of bar magnet
Magnetic dipole \[ = 100 \times 0.15\]
Magnetic dipole \[ = 15\,A{m^2}\]
The magnetic dipole of a bar magnet of geometric length \[18cm\] and pole strength
\[100Am\] is \[15\,A{m^2}\].

Thus, the correct answer is option A.

Note: While solving this problem, most of the students make mistakes while finding the magnetic dipole because they take the geometric length of the magnet into account. Rather we must take the magnetic length. This is due to the fact that poles of a bar magnet are present a little distance from the respective ends.