Derivation of expression for torque on rectangular coil in a magnetic field
Set up
- When current, I, flows through the coil, the conductor experiences a magnetic force.
- Force on side PQ = NBIbsinα (downwards) while Force on side RS = NBIbsinsα (upwards). The two forces cancel out due to rigidity of the coil.
- Side PS experiences force NBIacosα perpendicularly into the page while RQ experiences force NBIacosα perpendicularly out of page. The two forces constitute a couple whose moment of force
τ = F x b
= NBIabcosα
= NBIAcosα (where A is the area = a x b)
If θ is the angle between the field and the normal to the plane of the coil, then θ = 90° – α, and
τ = NBIAsinθ
The couple on the coil thus depends on the magnitude of the flux density B, the current I in it and the Area A, that is τ = mB sinθ, where m is the magnetic moment.
Dr. Bbosa Science
CATEGORIES General
TAGS Dr. Bbosa Science
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