Question

A magnet of magnetic moment $2J{T^{ - 1}}$ is aligned in the direction of magnetic field of $0.1T$ . What is the net work done to bring the magnetic moment normal to the magnetic field

(A) $0.1J$
(B) $0.2J$
(C) $1J$
(D) $2J$

Answer 1

Hint:
Here a magnet of a given magnetic dipole moment is aligned in the direction of the magnetic field that is at \[{0^0}\] and we have to find work done to bring this magnetic dipole moment at ${90^0}$ to the magnetic field. Use the formula of work done in terms of magnetic moment, magnetic field and the angle of direction between the two.




Complete step by step solution:
First start with the given information in the question:
Magnetic dipole moment is $2J{T^{ - 1}}$ .
Magnetic field strength is $0.1T$ .
Magnetic dipole moment is aligned in the direction of the magnetic field it means;
Initial angle, ${\theta _1} = {0^0}$
To bring magnetic dipole moment normal to the direction of magnetic field;
Final angle, ${\theta _2} = {90^0}$
Now, we know the formula for the work done in terms of magnetic dipole moment and magnetic field is given by:
$W = MB\left( {\cos {\theta _1} - \cos {\theta _2}} \right)$
Putting the values from the above;
$W = 2 \times 0.1\left( {\cos {0^0} - \cos {{90}^0}} \right)$
$W = 0.2J$

Hence the correct answer is Option(B).





Note:
 Here we have to bring the magnetic dipole moment to the normal to the direction of the magnetic field and we know that normal means perpendicular to each other hence the angle taken was ${90^0}$ . In the direction of the field means making an angle of ${0^0}$to each other hence the same direction.