Question

A bar magnet when placed at an angle of $${30}^{\circ }$$ to the direction of magnetic field of induction of $$5\times {10}^{-5}T$$, experiences a moment of a couple $$2.5\times {10}^{-6}N-m$$, If the length of the magnet is $$5cm$$ its pole strength is
A.$$2\times {10}^{-2}Am$$
B.$$5\times {10}^{-2}Am$$
C.$$2Am$$
D.$$5Am$$

Answer 1

Hint: Torque is defined as a coupled force acting on a body that causes a body to rotate about its axis.
Example: While opening a lead we apply coupled force (parallel, equal but in opposite direction ) to rotate it about its center.
Pole strength is a scalar quantity and it is defined as the strength of a bar magnet and its ability to attract other magnetic material towards itself and magnetic moment of a bar magnet is directly proportional to pole strength of a magnet.
Formula Used:
The torque acting on a bar magnet, $$\tau =MBsin\theta$$
Pole strength of bar magnet, $m={\displaystyle \frac{M}{L}}$

Complete answer:
Given that,
The angle of rotation, $$\theta ={30}^{\circ }$$
magnetic field of induction, $$B=5\times {10}^{-5}T$$
Torque, $$\tau =2.5\times {10}^{-6}N-m$$
Length of the magnet, $$L=5cm=0.05m$$
The net torque acting on a bar magnet is given as
$$\tau =MBsin\theta$$
Substituting the given values of τ, B, and θ we get
$$2.5\times {10}^{-6}=M\times 5\times {10}^{-5}\times sin30$$
$M={\displaystyle \frac{2.5\times {10}^{-6}}{sin30\times 5\times {10}^{-5}}}$
$M={\displaystyle \frac{2.5\times {10}^{-6}}{0.5\times 5\times {10}^{-5}}}$
$$\therefore M=0.1A{m}^2$$
Now the pole strength of a magnet is given as
$$M=mL$$
$$0.1=m\times 0.05$$
$\therefore m={\displaystyle \frac{0.1}{0.05}}=2\times {10}^{-3}=2mA$

Option C is correct among all.

Note:
In physics, torque is considered as a rotational analog of force, and it is expressed as $\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$.
Also, we must note that if we cut a bar magnet in half its pole strength will remain unaffected whereas its magnetic dipole moment will become half of its original intensity.