A wire carrying current I is tied between points P and Q and is in the shape of a circular arc of radius R due to a uniform magnetic field B (perpendicular to the plane of the paper, as shown in the figure) in the vicinity of the wire. If the wire subtends an angle 2 θ o at the center of the circle (of which it forms an arch) then the tension in the wire is:

Question

A wire carrying current I is tied between points P and Q and is in the shape of a circular arc of radius R due to a uniform magnetic field B (perpendicular to the plane of the paper, as shown in the figure) in the vicinity of the wire. If the wire subtends an angle 2 θ o at the center of the circle (of which it forms an arch) then the tension in the wire is:, I B R, I B R s i n θ 0, I B R 2 s i n θ 0, I B R θ 0 s i n θ 0

MARKS App · Accepted Answer

Consider any small element dl of arc of angle d θ . Then magnetic force d F = I d l . B outwards For equilibrium of element Idl B = 2 T sin dθ 2 For small angle sinθ ≃ θ I d l B = 2 T d θ 2 Idl B = T dl R T = I B R

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