Question

A magnet when placed perpendicular to a uniform field of strength ${10^{ - 4}}Wb/{m^2}$ experiences a maximum couple of moment $4 \times {10^{ - 5}}Nm$ . What is its magnetic moment?
A. $0.4A \times {m^2}$
B. $0.2A \times {m^2}$
C. $0.16A \times {m^2}$
D. $0.04A \times {m^2}$
E. $0.06A \times {m^2}$

Answer 1

Hint:
In case of a problem based on the magnetic field, we know that torque directly varies with the magnetic field. Also, we know for torque to be maximum, the angle between the plane of a bar magnet and a uniform field must be ${90^ \circ }$.There is a relation between magnetic moment and torque generated which we will use to get the solution of the given problem.



Complete step by step solution:
A magnet is placed in a uniform field of strength, $B = {10^{ - 4}}Wb/{m^2}$ (given)
A magnet experiences a maximum couple of moment i.e., torque ${\tau _{\max }} = 4 \times {10^{ - 5}}Nm$(given) and for maximum torque, $\theta = {90^ \circ }$
We know that, the formula for torque acting on a magnet in a uniform magnetic field is given as:
$\tau = \overrightarrow M \times \overrightarrow B = MB\sin \theta $
Here $M$ is magnetic dipole moment.
For calculating Magnetic moment, the formula will be:
$ \Rightarrow M = \dfrac{\tau }{{B\sin \theta }} = \dfrac{{{\tau _{\max }}}}{{B\sin \left( {{{90}^ \circ }} \right)}}$
Substituting all the required values from the question in the above expression, we get
$ \Rightarrow M = \dfrac{{4 \times {{10}^{ - 5}}}}{{{{10}^{ - 4}} \times (1)}}$ $(\therefore \sin {90^ \circ } = 1)$
$ \Rightarrow M = 4 \times {10^{ - 1}} = 0.4A \times {m^2}$
Thus, the magnetic moment of a magnet placed perpendicular in a uniform magnetic field is $0.4A \times {m^2}$.
Hence, the correct option is (A) $0.4A \times {m^2}$ .



Therefore, the correct option is A.




Note:
Since this is a problem related to uniform magnetic field and torque hence, quantities that are required to calculate the Magnetic Moment must be identified on prior basis as it gives better understanding of the problem and helps to further solve the question. Units must be there after each physical quantity.