In the diagram, `I_(1), I_(2)` are the strength of the currents in the loop and straight conductors respectively. OA = AB = R. The net magnetic field at the centre O is zero. Then the ratio of the currents in the loop and the straight conductors is

Options

A. `pi`
B. `2 pi`
C. `(1)/(pi)`
D. `(1)/(2 pi)`

Answer

D

Explanation

Magnetic field at the centre O due to current `I_(1)` in the loop is
`B_(1) = (mu_(0))/(4pi)(2pi I_(1))/(R )`
Magnetic field at the centre O due to current `I_(2)` through straight conductor is
`B_(2) = (mu_(0))/(4pi) (2l_(2))/(2R) = (mu_(0))/(4pi) (I_(2))/(R )`
As the net magnetic field at O is zero (given), therefore `B_(1) and B_(2)` are equal in magnitude and opposite in directions
`:. (mu_(0))/(4pi) (2pi I_(1))/(R ) = (mu_(0))/(4pi) (I_(2))/(R )`
`(I_(1))/(I_(2)) = (1)/(2pi)`