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(C) The magnetic field due to a long straight conductor at a distance $r$ is given by $B = \frac{\mu_0 I}{2 \pi r}$.For a conductor carrying current $

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$Y = \frac{I_1}{I_2} X$

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(C) The magnetic field due to a long straight conductor at a distance $r$ is given by $B = \frac{\mu_0 I}{2 \pi r}$.For a conductor carrying current $I_1$ along the $X$-axis,the magnetic field at a point $(x, y)$ is $B_1 = \frac{\mu_0 I_1}{2 \pi y}$ (directed perpendicular to the $XY$-plane).For a conductor carrying current $I_2$ along the $Y$-axis,the magnetic field at a point $(x, y)$ is $B_2 = \frac{\mu_0 I_2}{2 \pi x}$ (directed perpendicular to the $XY$-plane).For the net magnetic field to be zero,the magnitudes of the magnetic fields must be equal and opposite in direction: $B_1 = B_2$.$\frac{\mu_0 I_1}{2 \pi y} = \frac{\mu_0 I_2}{2 \pi x}$$\frac{I_1}{y} = \frac{I_2}{x}$Rearranging for $Y$,we get $Y = \frac{I_1}{I_2} X$.

Two long straight conductors with currents $I_1$ and $I_2$ are placed along $X$ and $Y$-axes respectively. The equation of the locus of points of zero magnetic induction is:

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