Question

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

• A. $0.5m$ from the 1st wire, towards the 2nd wire
• B. $0.2m$ from the 1st wire, towards the 2nd wire
• C. $0.1m$ from the 1st wire away from the 2nd wire
• D. $0.2m$ from the 1st wire, away from the 2nd wire

Answer 1

The correct option is C $0.1m$ from the 1st wire away from the 2nd wire

Force due to current carrying wire on another wire is given by $\frac{{\mu }_0{I}_1{I}_2}{2\pi r}$

Suppose wire is placed at a distance $x$ at left side of first wire carrying current $1A$

Let's assume new wire is carrying current $I$ A

Then force on new wire due to 1st wire $=\frac{{\mu }_0\times 1\times I}{2\pi x}$ ...............(1)

and due to second wire $=\frac{{\mu }_{0}I\times 2}{2\pi (x+0.1)}$............(2)

Since both wires are carrying current in different direction, there force on new wire will be in opposite direction

On equating (1) and (2)

$\frac{{\mu }_0\times 1\times I}{2\pi \times x}=\frac{{\mu }_0\times I\times 2}{2\pi (x+0.1)}$

On solving, we get $x=0.1m$