Question

Q. No. 7: A rectangular loop of cross-section area 'A', having 'N' turns and carrying a current of
l' amperes is held in a uniform magnetic field 'B'; (i) Write down the expression for the
maximum torque experienced by the loop.​

Answer 1

The expression for the maximum torque experienced by the loop. is τ= NiAB.

A rectangular loop of cross-section area 'A', having 'N' turns and carrying a current of 'l' amperes is held in a uniform magnetic field 'B', it will experience a torque.

Torque(τ) is a force that tends to cause rotation around the axis.

Torque is the cross product of the magnetic moment and  magnetic field vector.

τ = M × B

Magnetic moment (M) = NiA

∴τ= NiAB sinθ

(Where θ is the angle between the field and the normal to the coil)

This is the torque on a current carrying loop placed in a uniform magnetic field.

Maximum torque occurs when θ=90°, that is the loop is placed perpendicular to the magnetic field.

θ=90° ∴sinθ =1 (maximum)

In the case, torque will be:

τ= NiAB (maximum)

Torque experienced by the coil would be zero, when the coil is placed parallel or antiparallel to the direction of magnetic field.

Hence, the expression for the maximum torque experienced by the loop. is τ= NiAB.

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