The figure shows a circular wire loop of radius a and carrying a current i, which is placed in a perpendicular magnetic field B. (a) Consider a small part dl of the wire. Find the force on this part of the wire exerted by the magnetic field. (b) Find the force of compression in the wire.
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(a) Fdl=i×dl×B towards centre. (By cross product rule)
(b) Let the length of subtends an small angle of 2θ at the centre
Here,
2Tsinθ=i×dl×B
2Tθ=i×a×2θ×B [As θ→0,sinθ≈0]
T=i×a×B
T=a i B
Force of compression on the wire =iaB
Explanation:
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