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. When the system is put in uniform magnetic field of strength B going into the plane of the paper, the wire take the shape of a circle. The tension in the wire, after acquiring the circular shape is

Step-by-step solution

Given that, the length of wire =L Current passing through ring =I Let R be the radius of ring. Then, 2 R=L R= L 2 ...(i) Consider an element of ring A B which subtends an angle at the centre O , such that, A B= l=R ...(ii) If T be the tension at point P as shown in figure. We know that, force acting on element A B in uniform magnetic field, F=I B l ... (iii) (radially outward) By resolving tension into sine and cosine components T 2 is acting equal and opposite. So, it is cancelled. But sum of sine component is equ