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. $y=x{i}_1{i}_2$

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 $P(x,y)$ then
$B_{I_1}=B_{I_2}$ (Equating magnitudes)
$\frac{{\mu }_0}{2\pi }\frac{I_1}{y}=\frac{{\mu }_0}{2\pi }\frac{I_2}{x}\Rightarrow y=\frac{I_1}{I_2}x$