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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. 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:

IBL

IBLπ

IBL2π

IBL4π

Solution:

2Tsin(dθ/2) = BiRdθ
Tdθ = BiRdθ (for θ small)
T = BiR = BiL/(2π)