Question

Find the locus of points where the value of magnetic field is zero for the given current carrying configuration in the diagram where electric currents $i_{1}$ and $i_{2}$ are flowing in two mutually perpendicular conductors.

• A. $y=x$
• B. $y=\frac{i_{1}}{i_{2}}x$
• C. $y=\frac{x i_{2}}{i_{1}}$
• D. $y=xi_{1}i_{2}$

Answer 1

Answer: (B)

In first quadrant, magnetic field due to $I_{1}$ is outwards and due to $I_{2}$ it is inwards. So, net magnetic field may be zero.
Similarly, in third quadrant magnetic field due to $I_{1}$ is inwards and due to $I_{2}$ magnetic field is outwards.
Hence only in first and third quadrants magnetic field may be zero.
Let magnetic field be zero at point $P\left(\right.x,y\left.\right)$ then
$B_{I_{1}}=B_{I_{2}}$ (Equating magnitudes)
$\frac{\mu _{0}}{2 \pi }\frac{I_{1}}{y}=\frac{\mu _{0}}{2 \pi }\frac{I_{2}}{x}\Rightarrow y=\frac{I_{1}}{I_{2}}x$