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
B. 3
C. 2
D. 4

Answer

C

Explanation

When `kl_(2)` and `l_(2)` ar in the same direction
`(mu_(0))/(4pi) (2i_(1))/(r )-(mu_(0))/(4pi)(2i_(2))/(r )=10 mu T`
when `l_(1)` and `l_(2)` are n the opposite direction
`(mu_(0)2i_(1))/(4pir)+(mu_(0))/(4pi)(2i__(2))/(r )=30 muT`
on solving `l_(1)=20 A` and `l_(2)` are in the opposite direction
`(mu_(0)2l_(1))/(4pi r) +(mu_(0))/(4pi)(l_(1))/(r )=30muT`
on solving `l_(1)=20 A` and `l_(2)=10 A`
So `(l_(1))/(l_(2))=2`