1. Tardigrade
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  3. Physics
  4. 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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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 isPhysics Question Image

IIT JEEIIT JEE 2010

Solution:

$ \, \, \, \, \, \, \, \, \, \, \, \, L = 2 \pi R$
$\therefore \, \, \, \, \, \, \, R= L / 2\pi$
$ \, \, \, \, \, \, \, \, \, \, 2T sin(d heta) = F_m$
For small angles, $sin(d heta) \approx d heta$
$\therefore \, \, \, \, \, \, \, 2T (d heta) = I (dL) B \, sin \, 90^{\circ} $
$ \, \, \, \, \, \, \, \, \, \, \, \, \, = I (2R \, \cdot d heta) \cdot B$
$\therefore \, \, \, \, \, \, \, \, \, \, \, T = IRB = \frac{ILB}{2 \pi}$
$\therefore \, $ Correct option is (c)

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