Question

Two infinite wires, carrying currents $i_1$ and $i_2$, are lying along x- and y-axis, as shown in the x-y plane. Then,

• A. locus of points where $B$ is zero is a circle
• B. locus of points where $B$ is zero is a line
• C. $B$ decays hyperbolically along any line parallel to x-axis
• D. $B$ decays hyperbolically along any line parallel to y-axis

Answer 1

The correct option is B locus of points where $B$ is zero is a line

Let the co-ordinate of the point where B is zero be $(x,y).$
Magnetic field may be zero in first and third quadrants.

$\frac{{\mu }_0{i}_1}{2\pi y}=\frac{{\mu }_0{i}_2}{2\pi x}$ represents a straight line passing through the origin.

$\Rightarrow y=\frac{i_1}{i_2}x$ which is a straight line.