Torque on Bar Magnet in Magnetic Field

Torque on Bar Magnet in Magnetic Field:

Take a bar magnet NS of length 2l. Let ‘m’ be the strength of each pole.

Torque on Bar Magnet in Magnetic Field diagram - Torque on Bar Magnet in Magnetic Field
Torque on Bar Magnet - Torque on Bar Magnet in Magnetic Field

These two forces are equal and opposite and they act at different points. Hence they form the couple which tends to rotate the magnet clockwise.

Draw NA perpendicular on SA produced.

Torque acting on bar magnet (τ) will be given by
τ = Force x Perpendicular Distance
τ = mB x NA ……….(i)

From △NSA, NA/NS = Sin θ
⇒ NA = NS Sin θ
⇒ NA = 2l Sin θ

Therefore, τ = mB x 2l Sin θ
⇒ τ = (m x 2l) B Sin θ
⇒ τ = MB Sin θ (where M = m x 2l = magnetic dipole moment)
torque acting on bar magnet in vector form - Torque on Bar Magnet in Magnetic Field

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