Two long parallel wires separated by 0.1m carry currents of 1A and 2A respectively in opposite directions. A third current carrying wire parallel to both of them is placed in the same plane such that it feels no net magnetic force. It is placed at a distance of

Options

A. 0.5m from the `1^(st)` wire, towards the `2^(nd)` wire
B. 0.2m from the `1^(st)` wire, towards the `2(nd)` wire
C. 0.1m from the `1^(st)` wire, away from the `2^(nd)` wire
D. 0.2 m from the `1^(st)` wire, away from the `2^(nd)` wire.

Answer

C

Explanation

Suppose the third current carrying wire placed x cm from the first current-carrying wire.

Magnetic field due to first wire at the location of third wire, `vec(B)_(l)= (mu_(0)i_(1))/(2pi x) o.`
Magnetic field due to second wire at the location of third wire, `vec(B)_(2)= (mu_(0)i_(2))/(2pi (x+0.1)) ox`
Net magnetic field at the location of third wire would be zero if there is no net magnetic force,
`:. B_(1)= B_(2) rArr (mu_(0)i_(1))/(2pi x)= (mu_(0)i_(2))/(2pi (x+0.1)) [ :. i_(1) =1 A and i_(2)= 2A]`
`rArr (1)/(x)= (2)/(x+0.1) or x= 0.1m`