question_answer

Two long parallel wires P and Q are both perpendicular to the plane of the paper with distance 5 m between them. If P and Q carry current of 2.5 A and 5 A respectively in the same direction, then the magnetic field at a point half way between the wires is

A)  \[\frac{\sqrt{3}{{\mu }_{0}}}{2\pi }\]                     

B)         \[\frac{{{\mu }_{0}}}{\pi }\]

C)  \[\frac{3{{\mu }_{0}}}{2\pi }\]                  

D)         \[\frac{{{\mu }_{0}}}{2\pi }\]

Correct Answer: D

Solution :

Magnetic field at mid-point\[O\],                 \[\overset{\to }{\mathop{\mathbf{B}}}\,=\overset{\to }{\mathop{{{\mathbf{B}}_{1}}}}\,+\overset{^{\to }}{\mathop{{{\mathbf{B}}_{2}}}}\,\]                 \[=\frac{{{\mu }_{0}}}{2\pi }\frac{{{I}_{1}}}{r}-\frac{{{\mu }_{0}}}{2\pi }\frac{{{I}_{2}}}{r}\]                 \[=\frac{{{\mu }_{0}}}{2\pi }\frac{(2.5-5)}{2.5}\]                 \[=\frac{{{\mu }_{0}}}{2\pi }\]