Question

Two long straight conductors $AOB$ and $COD$ are perpendicular to each other and carry currents $i_1$ and $i_2.$ The magnitude of the magnetic induction at a point $P$ at a distance a from the point $O$ in a direction perpendicular to the plane $ABCD$ is

• A. $\frac{{\mu }_0}{2\pi a}(i_1+i_2)$
• B. $\frac{{\mu }_0}{2\pi a}\left(i_1-i_2\right)$
• C. $\frac{{\mu }_0}{2\pi a}\sqrt{\left(i_1^2+i_2^2\right)}$
• D. $\frac{{\mu }_0{i}_1{i}_2}{2\pi a\left(i_1+i_2\right)}$

Answer 1

Answer: (C)

Conductors $AOB$ and $COD$ are perpendicular to each other shown in figure.

At distance $a$ above $O,$
$B_1=\frac{{\mu }_0{i}_1}{2\pi a}$ and $B_2=\frac{{\mu }_0{i}_2}{2\pi a}$
$B_1$ is perpendicular to $B_2.$
Resultant of $B_1$ and $B_2,$
$B=\sqrt{B_1^2+B_2^2}$
$=\frac{{\mu }_0}{2\pi a}\sqrt{i_1^2+i_2^2}$