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 f

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:

TestHub · Accepted Answer

Consider any small elementdlof arc of angle $d θ$ . Then magnetic force $d F = I d l . B$ outwards

For equilibrium of element

$Idl B = 2 T sin \frac{dθ}{2}$

For small angle $sinθ ≃ θ$

$I d l B = 2 T \frac{d θ}{2}$

$Idl B = T \frac{dl}{R}$

$T = I B R$

Physics - Magnetism Question with Solution | TestHub

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