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Q.

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

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a

IBL

b

$\frac{I B l}{π}$

c

$\frac{I B l}{2 π}$

d

$\frac{I B l}{4 π}$

answer is C.

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Detailed Solution

Question Image

$Length of element A B = d l = r θ = (L / 2 π) θ .$

$Outward ampere force on AB is BIdl.$

$Inward force on A B due to tension T = 2 T \sin (θ / 2) = T θ .$

$Equating forces for equilibrium, T = BIL / 2 π .$

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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