Two parallel wires carrying equal currents `i_(1)` and `i_(2)` with `i_(1)gti_(2)`. When the current are in the same direction, the `10 mT`. If the direction of `i_(2)` is reversed, the field becomes `30 mT`. The ratio `i_(1)//i_(2)` is

Options

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

Answer

C

Explanation

`B_(1)=(mu_(0)i_(1))/(2pi.d/2)-(mu_(0)i_(2))/(2pi.d/2)=(mu_(0))/(pid)(i_(1)-i_(2))=10...(i)`

`B_(2)=(mu_(0))/(pid)(i_(1)+i_(2))=10...(ii)`
`(B_(1))/(B_(2))=(i_(1)-i_(2))/(i_(1)+i_(2))=10/30`
`i_(1)+i_(2)=3i_(1)-3i_(2) implies 2i_(1)=4i_(2)`
`(i_(1))/(i_(2))=4/2 =2`