Torque

Torque on a Rectangular Current Loop in a Uniform Magnetic Field

Considerations:

• A rectangular loop of length and breadth
• Current flows through the loop
• The loop is placed in a uniform magnetic field
• The angle between the magnetic field and the normal to the plane of the loop is

Step-by-Step Derivation:

Let the rectangular loop be placed in such a way that its plane makes an angle with the direction of the magnetic field .

Magnetic force on a current-carrying conductor of length is given by:

In a rectangular loop, the opposite sides experience equal and opposite forces, but these forces do not act along the same line. Hence, they form a couple which produces a torque.

Magnitude of Torque:

Let the area of the rectangular loop be:

Torque is given by:

Where:

• is the current
• is the area of the loop
• is the magnetic field strength
• is the angle between normal to the loop and the magnetic field

Vector Form:

Define the magnetic moment of the loop as:

(Direction of is given by the right-hand rule perpendicular to the plane of the loop)

Then, torque in vector form is:

Conclusion:

The torque acting on a rectangular current loop placed in a uniform magnetic field is:
, and in vector form,