A rectangular coil of N turns, length, L and breadth, b, carrying a current, I, is placed with its plane making a angle, θ, to a uniform magnetic field of flux density, B. Derive the expression for torque exerted on the coil.

A rectangular coil of N turns, length, L and breadth, b, carrying a current, I, is placed with its plane making a angle, θ, to a uniform magnetic field of flux density, B. Derive the expression for torque exerted on the coil.

• When current flows through the coil, the conductor experiences a magnetic force.
• Force on side PQ = NBIbsinθ (downwards) while Force on side RS = NBINsinθ (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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