question_answer

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

A)  zero              

B)  \[\frac{{{\mu }_{0}}i}{4\pi R}\]

C)  \[\frac{{{\mu }_{0}}i}{2\pi R}\]             

D)  \[\frac{{{\mu }_{0}}i}{\pi R}\]

Correct Answer: B

Solution :

 Magnetic field at mid point due to wire AB \[{{B}_{1}}=\frac{{{\mu }_{0}}i}{2\pi R}\] Magnetic field at midpoint due to wire CD \[{{B}_{2}}=\frac{{{\mu }_{0}}i}{2\pi R}\] Resultant of Magnetic field\[B={{B}_{1}}+{{B}_{2}}\] \[=\frac{{{\mu }_{0}}i}{2\pi R}+\frac{{{\mu }_{0}}i}{2\pi R}\] \[B=\frac{{{\mu }_{0}}i}{\pi R}\]