Question

A bar magnet of magnetic moment $200A - {m^2}$ is suspended in a magnetic field of intensity $0.25N/A - m$ . The couple required to deflect it through ${30^ \circ }$ is
A. $50N - m$
B. $25N - m$
C. $20N - m$
D. $15N - m$

Answer 1

Hint:
 When a bar magnet is suspended in a magnetic field of intensity, the two poles of the magnet experience a force. These experienced forces are equal in magnitude and opposite in direction. Thereby constituting a couple of forces that produce a torque. By applying the formula of torque we can calculate the desired deflection.

 Formula used:
The formula used to calculate the couple in the solution is: -
$\tau = \overrightarrow M \times \overrightarrow B = MB\sin \theta $
Here $\tau =$ Net force on magnet or Torque
$M=$ Magnetic moment
$B=$ Magnetic field of intensity
$\theta =$ Angle between the magnetic field and magnetic axes of the bar magnet




Complete step by step solution:
A bar magnet of magnetic moment $M = 200A - {m^2}$ is suspended in a magnetic field of intensity, $B = 0.25N/A - m$ (given)
Now we know that the formula for the torque acting on a magnet in a uniform magnetic field is given as:
$\tau = \overrightarrow M \times \overrightarrow B = MB\sin \theta $ … (1)
This magnet experiences a couple (or torque) in the magnetic field. Now to find out the couple required to deflect it through $\theta = {30^ \circ }$ we will take help from equation (1).
$ \Rightarrow \tau = MB\sin \theta $
Substituting all the required values from the question in the above expression, we get
$ \Rightarrow \tau = (200) \times 0.25 \times \sin \left( {{{30}^ \circ }} \right)$
$ \Rightarrow \tau = 50 \times 0.5 = 25N - m$ $\left( {\therefore \sin {{30}^ \circ } = \dfrac{1}{2} = 0.5} \right)$
Thus, the couple required to deflect a bar magnet through ${30^ \circ }$ is $25N - m$.
Hence, the correct option is (B) $25N - m$ .



Therefore, the correct option is B.




Note:
The alpha particles, beta particles and protons are charged particles, thereby being deflected by magnetic fields. Only gamma rays which are actually neutron particles are not deflected by magnetic fields as these particles have no charge. Neutron does not contain any electrical charge particles.