A bar magnet of magnetic moment M is placed in the magnetic field B. The torque acting on the magnet is:

A pair force is made up of two parallel forces that have the same magnitude but opposing directions and do not have the same path of action. A torque is produced by a pair force acting on a magnet with a magnetic moment (M) positioned in a magnetic field (B). The torque generated by the pair force is calculated as follows:

If τ is the torque and F is the magnitude of couple force and d is the perpendicular distance between the two couple force then,

τ = Fd

We know that if i is current, B is magnetic field, l is the length,

F=ilB

From using the two formulas stated above we can also state that, If b is the length of magnet/wire and sinθ is the sin of the angle between magnet/wire and couple force then,

τ=ilBbsinθ

The term ilb is the dipole moment (M)

. Hence, we can assert that,

τ = MBsinθ

⇒ τ=M×B

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