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in Physics by (60.2k points)

Figure (34-E10) shows a circular wire-loop of radius a, carrying a current i, 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 20 at the centre.

Here 2Tsinθ= i × dl × B

=> 2Tθ = i × a × 2θ × B [As θ  0, Sinθ ≈ 0]

=> T = i × a × B  dl = a × 2θ

Force of compression on the wire = iaB

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