Chapter: 11th 12th std standard Class Physics sciense Higher secondary school College Notes
Torque on a bar magnet placed in a uniform magnetic field
Torque on a bar magnet placed in a
uniform magnetic field
Consider a bar magnet NS of length 2l and pole strength m placed in a uniform magnetic field of induction B at an angle θ with the direction of the field (Fig.).
Due
to the magnetic field B, a force mB acts on the north pole along the direction
of the field and a force mB acts on the south pole along the direction opposite
to the magnetic field.
These
two forces are equal and opposite, hence constitute a couple.
The
torque τ due to the couple is
τ
= one of the forces ? perpendicular distance between them
τ
= F ? NA
= mB ? NA ...(1)
= mB ? 2l
sin θ
∴ τ = MB sin θ ...(2)
Vectorially
Vec
τ = Vec M ? Vec B
The
direction of τ is perpendicular to the plane containing Vec M and Vec B.
If
B = 1 and θ = 90o
Then from equation (2), τ
= M
Hence, moment of the magnet M is equal to the torque necessary to keep the magnet at right angles to a
magnetic field of unit magnetic induction.
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