Question

- A bar magnet of magnetic
moment 100 Am is bent at of
mid point such that the two
Parts make an angle of 6o. The
new magnetic moment is.​

Answer 1

Given :

Magnetic moment of the bar magnet = 100 Am

After bending at its mid point the angle between the two parts = 60°

To Find :

New magnetic for this system = ?

Solution :

We know that the magnetic moment for a bar magnet which have pole strength 'm' and distance between the poles of the magnet 'l' is given as :

$M= ml$  -(1)  

Now if $P_1$ and $P_2$ are the magnetic  dipole moments of the two sections , then :

$\vec P = \vec P_1 + \vec P_2$

Or, $|\vec P|= \sqrt{P_1^2 + P_2^2 + 2 P_1 P_2cos \theta}$

Here , $|\vec P_1| = |\vec P_2|$   , which is  equal to half of the magnetic moment of the bar magnet .

So, $|\vec P_1| = |\vec P_2| = \frac{1}{2} \times 100 Am$

                       = 50 Am

So, $|\vec P| = \sqrt{50^2 +50 ^2 + 2 \times 50 \times 50 \times cos 120}$

           $= \sqrt{2500 + 2500 + 2 \times 2500 \times \frac{-1}{2}}$

           $=\sqrt{2500 + 2500 - 2500}$

           =  $\sqrt{2500}$

          = 50 Am

So, the new magnetic moment  is 50 Am.