A bar magnet of length 10 cm and having the pole strength equal 10^3 Am to is kept in a magneti

step 1 So, let's solve this question. In SI unit, your pole length is ampere per meter. Here, the pole

A bar magnet of length 10 cm and having the pole strength...

$\mathrm{A}$ bar magnet of length $10 \mathrm{~cm}$ and having the pole strength equal $10^{3} \mathrm{Am}$ to is kept in a magnetic field having magnetic induction (B) equal to $4 \pi \times 10^{3}$ tesla. It makes an angle of $30^{\circ}$ with the direction of magnetic induction. The value of the torque acting on the magnet is Joule. (a) $2 \pi \times 10^{-7}$ (b) $2 \pi \times 10^{5}$ (c) $0.5$ (d) $0.5 \times 10^{2}$

$\mathrm{A}$ bar magnet of length $10 \mathrm{~cm}$ and having the pole strength equal $10^{3} \mathrm{Am}$ to is kept in a magnetic field having magnetic induction (B) equal to $4 \pi \times 10^{3}$ tesla. It makes an angle of $30^{\circ}$ with the direction of magnetic induction. The value of the torque acting on the magnet is

Joule.
(a) $2 \pi \times 10^{-7}$
(b) $2 \pi \times 10^{5}$
(c) $0.5$
(d) $0.5 \times 10^{2}$

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Key Concepts

Trigonometric Function in Torque Calculations

The sine function, sin?, in the torque expression quantifies the relationship between the angle of the magnetic dipole with respect to the magnetic field direction and the effectiveness of the field in producing torque. For instance, a 30° angle leads to sin 30° = 0.5, showing that only half of the maximum possible torque is produced at this orientation.

Magnetic Torque

The torque acting on a magnetic dipole in a magnetic field is given by the vector cross product ? = mB sin?, where m is the magnetic dipole moment, B is the magnetic field strength, and ? is the angle between the vectors m and B. This concept is central to understanding how dipoles interact with external magnetic fields and how they experience rotational forces.

Magnetic Dipole Moment

For a bar magnet, the magnetic dipole moment is calculated as the product of the pole strength and the distance between the poles. It represents the strength and orientation of a magnet's magnetic field and is a key quantity when determining the torque experienced by the magnet in an external field.

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