A bar magnet of length 10 cm and having pole strength equal to 10^-3 Wb is kept in a magnetic

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 pole strength equal...

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

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

Key Concepts

Angular Dependence in Magnetic Interactions

In the context of a magnetic dipole interacting with a magnetic field, the torque is directly proportional to the sine of the angle between the dipole moment and the magnetic field. This angular dependence is critical because it determines the effective component of the dipole moment that interacts with the magnetic field, thereby influencing the resulting torque.

Magnetic Field (Magnetic Induction)

This represents a region around a magnet within which magnetic forces can be observed. It is quantified in teslas (T) and directly influences the behavior of magnetic dipoles, including the magnitude of the torque they experience when immersed in the field.

Torque on a Magnetic Dipole

A magnetic dipole in a uniform magnetic field experiences a torque that tends to align the dipole with the field. The magnitude of this torque is given by the product of the magnetic dipole moment, the magnetic field strength, and the sine of the angle between them (? = mB sin?), illustrating the dependence on the orientation with respect to the field.

Magnetic Dipole Moment

This is a measure of the strength and orientation of a magnet’s ability to produce a magnetic field. It is generally defined as the product of the magnetic pole strength and the distance between the poles, and it determines how the magnet interacts with external magnetic fields.

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