Q. Two long straight wires are set parallel to each other. Each carries a current $i$ in the opposite direction and the separation between them is $2R.$ The intensity of the magnetic field midway between them is
Explanation
(d) Magnetic field at mid-point due to wire $AB$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B_{1} = \frac{\mu_{0}i}{2\pi R}$
Magnetic field at mid-point due to wire $CD$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B_{2} = \frac{\mu_{0}i}{2\pi R}$
Resultant of Magnetic field $B = B_{1} + B_{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{\mu_{0}i}{2\pi R} + \frac{\mu_{0}i}{2\pi R}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B = \frac{\mu_{0}i}{\pi R}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.