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(C) Let the two conductors lie in the $X-Y$ plane. Let the conductor carrying current $I_1$ be along the $X$-axis and the conductor carrying current $

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straight line passing through the point of intersection of the conductors.

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(C) Let the two conductors lie in the $X-Y$ plane. Let the conductor carrying current $I_1$ be along the $X$-axis and the conductor carrying current $I_2$ be along the $Y$-axis.At any point $(x, y)$ in the plane,the magnetic field $B_1$ due to the wire along the $X$-axis is $B_1 = \frac{\mu_0 I_1}{2 \pi y}$ (directed perpendicular to the plane).The magnetic field $B_2$ due to the wire along the $Y$-axis is $B_2 = \frac{\mu_0 I_2}{2 \pi x}$ (directed perpendicular to the plane).For the net magnetic induction to be zero,the magnitudes must be equal and directions must be opposite: $B_1 = B_2$.$\frac{\mu_0 I_1}{2 \pi y} = \frac{\mu_0 I_2}{2 \pi x}$.Rearranging the terms,we get $y = \left( \frac{I_1}{I_2} \right) x$.This is the equation of a straight line passing through the origin (the point of intersection of the conductors).

Two mutually perpendicular conductors carrying currents $I_1$ and $I_2$ lie in one plane. The locus of the point at which the magnetic induction is zero,is a

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