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. $\frac{\mu_0}{2 \pi a}\left(i_1+i_2\right.)$
• 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. $\frac{\mu_0 \quad i_1 i_2}{2 \pi a\left(i_1+i_2\right)}$

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 $B_{2},$
$B=\sqrt{B_{1}^{2} + B_{2}^{2}}$
$= \, \frac{\mu _{0}}{2 \pi a}\sqrt{i_{1}^{2} + i_{2}^{2}}$