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Torque on rectangular coil in a magnetic field

Torque on rectangular coil in a magnetic field in Grade 12 Physics

Torque on the rectangular coil in a magnetic field

tight binding approximation

The torque on a rectangular coil in a magnetic field is explained below:

As the current-carrying conductor experiences a force when placed in a magnetic field, each side of a current-carrying rectangular coil experiences a force in a magnetic field. In the present section, we shall see in what way the rectangular loop carrying current is influenced by a magnetic field.

Consider a rectangular coil of length l and breadth b carrying a current I placed in a uniform magnetic field B. θ be the angle between the plane of rectangular coil and magnetic field. The magnitude of experience by each side of the loop is given below.

· Force acting on side PQ (F1):

torque

the direction of force is perpendicular to the plane containing PQ and B. It is directed outward direction as shown in the figure.

· Force acting on side QR (F2):

 

The direction of force is perpendicular to the plane containing QR and B. It is directed downward direction as shown in the figure.

· Force acting on side RS (F3):
torque

The direction of force is perpendicular to the plane containing RS and B. It is directed inward direction as shown in the figure.

· Force acting on side SP (F4):

Torque on rectangular coil in a magnetic field

The direction of force is perpendicular to the plane containing SP and B. It is directed upward direction as shown in the figure.

As the force acting on the upper and lower sides are equal and opposite along the same line of action, they cancel each other. As the force acting on the sides QR and SP are equal and opposite along different lines of action they constitute a couple. Hence the rectangular coil experiences a torque.

Therefore the magnitude of torque acting on the coil is
Torque on rectangular coil in a magnetic field

If the rectangular coil having N number of turns then torque is given by
Torque on rectangular coil in a magnetic field

Thus the torque acting on a coil in a magnetic field depends on the number of turns, area of the current loop, the strength of the current, and magnetic field.

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