Question

Two infinitely long straight wires lie in the x-y plane along x and y axes, respectively. Each wire carries a current i, respectively, in positive of x and y axes. The locus of points, where the magnetic field is zero is

• A. $y^2=x$
• B. $x=y^2$
• C. $x-y=0$
• D. $x+y=0$

Answer 1

The correct option is C $x-y=0$

Given: $I_1=I_2=i$

Solution: Here we are going to apply right hand thumb rule,

which conclude that magnetic field vanishes

in region $I$ and $III$.

Now, Let the magnetic field at point $P(x,y)$ is zero.

So, magnetic field due to current $I_1$ is:

$B_1=\frac{{\mu }_0{I}_1}{2\pi x}$ (directly outward)

$==>B_1=\frac{{\mu }_{0}i}{2\pi x}$ (directly outward)

and, magnetic field due to current $I_2$ is:

$B_2=\frac{{\mu }_0{I}_2}{2\pi y}$ (directly inward)

$==>B_2=\frac{{\mu }_{0}i}{2\pi y}$ (directly inward)

As field is vanishes,

So, $B_1=B_2$

$==>\frac{{\mu }_{0}i}{2\pi x}=\frac{{\mu }_{0}i}{2\pi y}$

$==>x=y$

$x-y=0$

hence,

The correct opt : C