Question

Two identical thin bar magnets each of length \[l\] and pole strength \[m\] are placed at right angle to each other with north pole of one touching south pole of the other. Magnetic moment of the system is:
A. \[ml\]
B. \[2ml\]
C. \[\sqrt 2 ml\]
D. \[\dfrac{{ml}}{2}\]

Answer 1

Hint:
When two identical thin bar magnets are placed at right angle to each other with the north pole of one touching the south pole of another magnet, then behaviour of the overall system is found to be like a magnet. Therefore by placing them at right angles we can determine the magnetic moment of the system. We can use Pythagoras theorem for right angle triangles.


Formula used:
\[M = m \times l\]; \[M\]- magnetic dipole moment, \[m\]- pole strength and \[l\]- length between the dipoles.

Complete step by step solution:
Let us begin to solve this question. For that we have to portray the figure about the given statement in the question as below:


Now, it has been asked to find the magnetic moment of the whole system. So we have to use the above figure for finding the distance between two poles of two bar magnets which are not touching each other. For that we have to consider the above right angled triangle and calculate the hypotenuse that is AC.
By using Pythagoras theorem, we get
\[A{C^2} = A{B^2} + B{C^2}\]
\[AC = \sqrt {A{B^2} + B{C^2}} \]
\[AC = \sqrt {{l^2} + {l^2}} \]
\[\therefore AC = \sqrt 2 l\]
So, the length of the magnet system is \[\sqrt 2 l\], so, the magnetic moment is given by:
\[M = m \times \sqrt 2 l\]
\[\therefore M = \sqrt 2 ml\]
So, the magnetic dipole moment of the new dipole of the system of two magnets is \[\sqrt 2 ml\]
Correct answer is option c.




Therefore, the correct option is C.




Note:
 A thin magnet is actually a magnetic dipole and that is comparable to an electric dipole of two equal and opposite charges. Only the isolated magnetic charges are not found in nature. Even if a bar magnet is cutting to its atomic level, both the south and north poles can never be separated.