The torque on a current loop is a fundamental concept in electromagnetism, playing an important role in the operation of electric motors and other electromagnetic devices. When a current-carrying loop is placed in an external magnetic field, it experiences a torque that tends to align the loop’s magnetic moment with the magnetic field. This phenomenon can be described mathematically using the following formula:

Torque (τ) = μ x B

Where:

- τ is the torque vector experienced by the current loop
- μ is the magnetic moment vector of the current loop
- B is the magnetic field vector
- x denotes the vector cross product

The magnetic moment (μ) of a current loop is defined as the product of the current (I) flowing through the loop, the loop’s area (A), and the unit vector (n) perpendicular to the plane of the loop:

μ = IAn

The torque on the current loop can be calculated using the cross product formula:

τ = IA(n x B)

The resulting torque vector is perpendicular to both the magnetic moment vector and the magnetic field vector, following the right-hand rule. The magnitude of the torque can be expressed as:

|τ| = IA|B|sinθ

Where:

- |τ| is the magnitude of the torque
- |B| is the magnitude of the magnetic field
- θ is the angle between the magnetic moment vector (μ) and the magnetic field vector (B)

The torque on a current loop is responsible for the rotational motion observed in devices such as electric motors. When a current loop is placed in a magnetic field, the torque causes the loop to rotate, aligning its magnetic moment with the magnetic field. This principle is the basis for the operation of many electromagnetic devices and has numerous practical applications in modern technology.