The torque acting on a magnetic dipole in a magnetic field can be expressed using the formula

where $\tau$ represents the torque, $\mathbf{m}$ denotes the magnetic dipole moment, and $\mathbf{B}$ signifies the magnetic field strength.

To fully grasp this formula, it is essential to first understand the concept of a magnetic dipole moment. The magnetic dipole moment quantifies the strength and orientation of a magnetic dipole, which consists of a pair of opposite magnetic poles separated by a certain distance. It is defined as the product of the strength of each pole and the distance between them, and is commonly represented by the symbol $\mathbf{m}$.

When a magnetic dipole is positioned within a magnetic field, it experiences a torque, which is a rotational force that aims to align the dipole with the direction of the magnetic field. The magnitude of this torque is directly proportional to the product of the magnetic dipole moment and the magnetic field strength, as given by the equation

In this context, the symbol $\times$ indicates the vector cross product.

To compute the torque on a magnetic dipole using this formula, it is crucial to know both the magnitude and direction of 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, which can be determined using the right-hand rule. Specifically, if you point your right thumb in the direction of the magnetic field $\mathbf{B}$ and curl your fingers in the direction of the magnetic dipole moment $\mathbf{m}$, your thumb will indicate the direction of the torque $\tau$, which is orthogonal to both vectors.