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Question
A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is ______.
Options
IBL
`"IBL"/pi`
`"IBL"/(2pi)`
`"IBL"/(4pi)`
Solution
A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is `bbunderline("IBL"/(2pi))`.
Explanation:
2T sin`("d"theta)/2` = BIRdθ
T dθ = BIRdθ (for θ small)
T = BIR = `"BIL"/(2pi)`
