question_answer

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

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

B) \[\frac{{{\mu }_{\operatorname{o}}}}{\pi }\]   

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

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

Correct Answer: D

Solution :

At point p \[{{\vec{B}}_{P}}=\frac{m\times 2.5}{2\times 2.5}=\frac{2{{m}_{o}}}{2p}\,\,\otimes \,\,\,into\,the\,\,plane\] \[{{\vec{B}}_{P}}=\frac{\mu \times 5}{2\times 2.5}=\frac{2{{\mu }_{\operatorname{o}}}}{2\pi }\,\,\odot \,\,\,\operatorname{out}\,of\,\,plane\] \[{{\vec{B}}_{net}}={{\vec{B}}_{Q}}-\vec{B}p{{\vec{B}}_{Q}}>{{\vec{B}}_{P}}\] \[=\frac{{{\mu }_{\operatorname{o}}}}{2\pi }\]