A wire carrying current I is tied between points P and Q and is in the shape of a circular arch of radius R due to a uniform magnetic field B (perpendicular to the plane of the paper, shown by cross marked) in the vicinity of the wire. If the wire subtends and angle `2 theta_(0)` at the centre of the circle of which it forms an arch) then the tension in the wire is:

Options

A. IBR
B. `(IBR)/(sin theta_(0))`
C. `(IBR)/(2 sin theta_(0))`
D. `(IBR theta_(0))/(sin theta_(0))`

Answer

a

Explanation

Net magnetic force on wire inside uniform magnetic field depends on the direct distance between two ends of wire. Let `F_(m)` . be the magnetic force on given section of wire and be the tension Tension acts along the tangent to the circular arc as shown in figure.

For wire to remain in equilibrium we can write the following equation.
`2F sin theta_(0) = F_(m)`
` 2F sin theta_(0) = i (2 R sin theta) B`
`rArr " " F = iRB`
Hence option (a) is correct.