Q. Two identical long conducting wires AOB and COD 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 :
A) $\frac{\mu_0}{2\pi d}\left(\frac{I_1}{I_2}\right)$
B) $\frac{\mu_0}{2\pi d}(I_1 + I_2)$
C) $\frac{\mu_0}{2\pi d}(I_1^2 - I_2^2)$
D) $\frac{\mu_0}{2\pi d}(I_1^2 + I_2^2)^{1/2}$
Explanation
[Solution] Each wire gives $\frac{\mu_0 I}{2\pi d}$ at P, and the two fields are perpendicular, so $B = \frac{\mu_0}{2\pi d}\sqrt{I_1^2 + I_2^2}$. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.