Electromagnetic Induction and Alternating Current 7 Question 8
8. 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
(2010)
(a) $I B L$
(b) $\frac{I B L}{\pi}$
(c) $\frac{I B L}{2 \pi}$
(d) $\frac{I B L}{4 \pi}$
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Answer:
Correct Answer: 8. (c)
Solution:
$$ \begin{aligned} L & =2 \pi R \\ R & =L / 2 \pi \\ 2 T \sin (d \theta) & =F _m \end{aligned} $$
For small angles, $\sin (d \theta) \approx d \theta$
$$ \begin{aligned} & \therefore \quad 2 T(d \theta)=I(d L) B \sin 90^{\circ} \\ & =I(2 R \cdot d \theta) \cdot B \\ & \therefore \quad T=I R B=\frac{I L B}{2 \pi} \end{aligned} $$
