Question

 A long magnet is cut in two parts in such a way that the ratio of their lengths is \[2:1\]. The ratio of pole strengths of both the section is:
A. Equal
B. In the ratio of \[2:1\]
C. In the ratio of \[1:2\]
D. In the ratio of \[4:1\]

Answer 1

Hint:
When a long magnet is cut into two equal halves, then these two halves will have a south pole and also a north pole. It is found by several experiments that the pole strength of each piece is perpendicular to its length which is exactly the same as the pole strength of the original long magnet.


Complete step by step solution:
 Let us understand the concept to be used here first. It has been asked that if the magnet is cut into the ratio of \[2:1\]then what will be the ratio of the pole strength of these magnets. For this:
We have magnetic dipole moment as the product of pole strength and length of the magnet. Mathematically is shown as:
\[M = m \times l\]; … \[eq(1)\]
\[M\]- magnetic dipole moment, \[l\] is the length of the magnet and \[m\]is magnetic strength.
Therefore,
\[m = \dfrac{M}{l}\]
This means magnetic pole strength is equal to the magnetic dipole moment per unit length.
Hence, when we take a bar magnet with length \[l\] and cut it into the ratio of \[2:1\] then the new lengths are \[\dfrac{{2l}}{3},\dfrac{l}{3}\].
So the new dipole moment is \[{M_1}\]and \[{M_2}\]
Thus, by replacing \[l\] in \[eq(1)\] with new lengths and new magnetic dipole moments we get,
\[{M_1} = m\left( {\dfrac{{2l}}{3}} \right)\] and \[{M_2} = m\left( {\dfrac{l}{3}} \right)\]
So the conclusion here is that the magnetic dipole moment changes and the magnetic pole strength remains unchanged that means
The correct answer is option a.




Therefore, the correct option is A.




Note:
To approach this type of problem we should always remember whenever a long magnet is cut transverse to its length , then pole strength of each piece is always the same but only their magnetic moment is going to be halved as the length of the original magnet is halved.