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

• A. IBL
• B. $\frac{IBL}{\pi}$
• C. $\frac{IBL}{2 \pi}$
• D. $\frac{IBL}{4 \pi}$

Answer 1

Answer: (C)

$\frac{IBL}{2 \pi}$

Answer 2

$\, \, \, \, \, \, \, \, \, \, \, \, L = 2 \pi R$
$\therefore \, \, \, \, \, \, \, R= L / 2\pi$
$\, \, \, \, \, \, \, \, \, \, 2T sin(d heta) = F_m$
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)