The figure shows a circular loop of radius a with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is d. The loop and the wires are carrying the same current I. The current in the loop is in the counter – clockwise direction if seen from above:

Consider `d gt gt a`, and the loop is rotated about its diameter parallel to the wires by `30^(@)` from the position shown in the figure. If the currents in the wires are in the opposite directions, the torque on the loop at its new position will be (Assume that the net field due the wires is constant over the loop):

Options

A. `(mu_(0)I^(2)a^(2))/d`
B. `(mu_(0)I^(2)a^(2))/(2d)`
C. `(sqrt3mu_(0)I^(2)a^(2))/d`
D. `(sqrt3mu_(0)I^(2)a^(2))/(2d)`

Answer

B

Explanation

Magnetic field at mid point of two wires `=(mu_(0)l)/(pid)o x`
Magnetic moment of loop `=lpia^(2)`
Torque on loop `=M B sin 150^(@)`
`=(mu_(0)I^(2)a^(2))/(2d)`