Question

A bar magnet of geometric length $ 18m $ has pole strength of $ 100Am $ . Then the magnetic dipole moment of the magnet is:
(A) $ 9A{m^2} $
(B) $ 15A{m^2} $
(C) $ 18A{m^2} $
(D) $ 30A{m^2} $

Answer 1

Hint :We know that the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Now we have to find the magnetic dipole moment of the magnet by using the formula of $ M = m \times 2L $
Where, $ M $ is the magnetic moment, $ m $ is the pole strength and $ 2L $ is the length of the magnet.

Complete Step By Step Answer:
According to the given data, we have magnetic dipole moment of the bar magnet as:
 $ M = m \times 2L $ …. $ (1) $
And the magnetic length is the $ \dfrac{5}{6}th $ part of the geometric length of the magnet, i.e. we have
Magnetic length $ \left( {2L} \right) $ $ = \dfrac{5}{6}(geometric - length) $ ….. $ (2) $
Thus, from equations $ (2) $ , we get
 $ \Rightarrow 2L = \dfrac{5}{6} \times 18 $ …. (Since, the geometric length of magnet is given) $ (3) $
Thus, from $ (1) $ and $ (3) $ , we get
 $ \Rightarrow M = 100 \times \dfrac{5}{6} \times 18cm $
 $ \Rightarrow M = 100 \times 0.15m $ …. (Conversion from centimeter to meter)
 $ \therefore M = 15A{m^2} $
Therefore, the magnetic moment of the given bar magnet is $ 15A{m^2} $
The correct answer is option B.

Note :
The magnetic strength is defined as the physical quantity that is used as one of the basic measures of the intensity of the magnetic field. The magnetic pole strength is defined as the strength of the north pole is taken to be $ + qm $ and that of the south pole is chosen as $ - qm $ . Also, the pole strength of a magnet is given by the ratio of magnetic moment to its effective length (called the magnetic length). When we understand that the magnetic moment is, we can calculate the answer of this question.