A rectangular coil of N turns each of length, L, and breadth, b, is inclined at an angle θ to a uniform magnetic field of flux density B. Derive an expression for torque of the coil when a current I is passed through it.

A rectangular coil of N turns each of length, L, and  breadth, b, is inclined at an angle θ to a uniform magnetic field of flux density B. Derive an expression for torque of the coil when a current I is passed through it.

• When current flows through the coil, the conductor experiences a magnetic force.
• Force on side PQ = NBIbsinθ (downwards) while Force on side RS = NBIbsinθ (upwards). The two forces cancel out due to rigidity of the coil.
• Side PS experiences force NBIL perpendicularly into the page while RQ experiences force NBIL perpendicularly out of page. The two forces constitute a couple whose moment of force

T = F x bcosθ

= NBILbcosθ

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