Two mutually perpendicular conductors carrying currents I1 and I2 lie in one plane. Locus of the point at which the magnetic induction is zero, is a

Two mutually perpendicular conductors carrying currents I₁ and I₂ lie in one plane. Locus of the point at which the magnetic induction is zero, is a

A
circle with centre as the point of intersection of the conductor.
B
parabola with vertex as the point of intersection of the conductors
C
straight line passing through the point of intersection of the conductors.
D
rectangular hyperbola

Solution:

Let wire -1 lie along x-axis and wire -2 lie along y-axis .

If at point (x,y) magnetic field is zero . then

$\frac{μ_{0} i_{1}}{2 πy} - \frac{μ_{0} i_{2}}{2 πx} = 0 \Rightarrow y = \frac{i_{1}}{i_{2}} x$

$which is a straight line passing through the origin .$

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