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PhysicsSingle correct+3 / -1Question 62 of 84

IIT-JEE 2010 · Paper 1, Physics question 62

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

Left: a loose closed loop of wire with its two ends at adjacent fixed points (dots), current clockwise. Right: in a uniform field into the page (crosses), the same wire forms a circle with the ends at the bottom.
Choose one option
Answer and worked solution

Official answer: C

Circle. The wire of length LL forms a circle of radius r=L2πr=\dfrac L{2\pi}, pushed outward by the magnetic force (current clockwise, field into the page).

Small element. An arc subtending dθd\theta carries force BI r dθBI\,r\,d\theta outward, balanced by the two tensions, whose inward resultant is T dθT\,d\theta:
T dθ=BIr dθ  ⟹  T=BIr=IBL2π.T\,d\theta=BIr\,d\theta\implies T=BIr=\frac{IBL}{2\pi}.

(C)

Topics:Force on a current-carrying conductor
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