Question

two mutually perpendicular conductors carrying current i1 and i2 lie in one plane .if i1 is taken along x axis and i2 along y axis the locus of points where magnetic induction is zero is

Answer 1

Magnetic field in X-Y plane at position (x,y) due to both wires must be zero

current carrying wire with current i1 is taken along X axis

now the magnetic field at the given point is

$B_1 = \frac{\mu_0 i_1}{2\pi y}$

now at the same point the magnetic field due to other wire placed along Y axis is given by

$B_2 = \frac{\mu_0 i_2}{2\pi x}$

now we have to make the magnitude of magnetic field due to both wires same

$B_1 = B_2$

$\frac{\mu_0 i_1}{2 \pi y} = \frac{\mu_0 i_2}{2 \pi x}$

now by solving above we have

$y = \frac{i_1}{i_2} x$

so its a straight line with slope i1/i2 and passing from origin