Two identical long conducting wires $A O B$ and $C O D$ are placed at right angle to each other, wit

Question

Two identical long conducting wires $A O B$ and $C O D$ are placed at right angle to each other, with one above other such that $O$ is their common point for the two. The wires carry $I_{1}$ and $I_{2}$ currents, respectively. Point $P$ is lying at distance $d$ from $O$ along a direction perpendicular to the plane containing the wires. The magnetic field at the point $P$ will be\

Professor PC Thomas Classes · Answer

(d) : The magnetic field at the point $P$, at a perpendicular distance $d$ from $O$ in a direction perpendicular to the plane $A B C D$ due to currents through $A O B$ and $C O D$ are perpendicular to each other. Hence,\ $B=\left(B_{1}^{2}+B_{2}^{2}ight)^{1 / 2}$\ $=\left[\left(\frac{\mu_{0}}{4 \pi} \frac{2 I_{1}}{d}ight)^{2}+\left(\frac{\mu_{0}}{4 \pi} \frac{2 I_{2}}{d}ight)^{2}ight]^{1 / 2}$\ $=\frac{\mu_{0}}{2 \pi d}\left(I_{1}^{2}+I_{2}^{2}ight)^{1 / 2}$\