Two mutually perpendicular conductors carry currents $i_{1}$ and $i_{2}$ along x-axis and y-axis respectively. The locus of the points at which magnetic induction is zero.

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$y = \frac{i_{1}}{i_{2}} x$

$x^{2} + y^{2} = \frac{i_{1}}{i_{2}}$

$x = \frac{i_{1}}{i_{2}} y$

$y = \frac{i_{2}^{2}}{i_{1}} x$

answer is B.

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Detailed Solution

$B = \frac{μ_{0} i}{2 π r}$

field due to conductor along y axis

$\frac{μ_{0} i_{2}}{2 π x} i n w a r d$

$f i e l d d u e t o c o n d u c t o r a l o n g x a x i s \frac{μ_{0} i_{1}}{2 π y} o u t w a r d$

for zero field

$y = \frac{i_{1}}{i_{2}} x$

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