How do you calculate the torque on a magnetic dipole in a magnetic field?

The torque on a magnetic dipole in a magnetic field can be calculated using the formula τ = m × B, where m is the magnetic dipole moment and B is the magnetic field strength.

To understand this formula, it is important to first understand what a magnetic dipole moment is. A magnetic dipole moment is a measure of the strength and orientation of a magnetic dipole, which is a pair of opposite magnetic poles separated by a distance. It is defined as the product of the strength of each pole and the distance between them, and is usually represented by the symbol m.

When a magnetic dipole is placed in a magnetic field, it experiences a torque, or turning force, that tends to align it with the direction of the magnetic field. The magnitude of this torque is proportional to the product of the magnetic dipole moment and the magnetic field strength, and is given by the formula τ = m × B, where × represents the vector cross product.

To calculate the torque on a magnetic dipole using this formula, you need to know the magnitude and direction of both the magnetic dipole moment and the magnetic field. The direction of the torque is perpendicular to both the magnetic dipole moment and the magnetic field, and is determined by the right-hand rule. If you point your right thumb in the direction of the magnetic field and your fingers in the direction of the magnetic dipole moment, the direction of the torque will be perpendicular to both.