Two parallel long wires carry currents `i_(1) "and" i_(2)` with `i_(1) gt i_(2)`.When the currents are in the same direction then the magnetic field midway between the wires is `10 mu T.` when the direction of `i_(2)` is reversed ,then it becomes `40 mu T.` then ratio of `i_(1)//i_(2)` is

Options

A. `1/2`
B. `2/3`
C. `3/4`
D. `3/2`

Answer

D

Explanation

When the currents flow in the same direction.
`(because i_(1) gt i_(2))`
The magnetic field at O is given by
`B_(1) =(+ mu_(0)i_(1))/(2pi(r//2))-(mu_(0)i_(2))/(2pi(r//2))`
`=(mu_(0))/(pir)(i_(1) -i_(2)) =6xx10^(-6)T`

When they flow in opposite directions
`B_(2) =(mu_(0))/(pir) (i_(1) +i_(2)) =3xx 10^(-5)T`
`therefore (B_(2))/(B_(1))=(3xx 10^(-5))/(6xx10 ^(-6))=30/6 =5/1 =(i_(1) +i_(2))/(i_(1) -i_(2))`
`therefore 5i_(1) -5i_(2) =i_(1) +i_(2) therefore 4i_(1) =6i_(2) " "therefore (i_(1))/(i_(2))=3/2`