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 amp and 5 amp respectively in the same direction, then the magnetic field at a point half way between the wires is                                 [Kerala PMT 2005]

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

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

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

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

E) (e)     \[\frac{\sqrt{3}{{\mu }_{0}}}{\pi }\]

Correct Answer: D

Solution :

                   In the following figure magnetic field at mid point M is given by \[{{B}_{net}}={{B}_{Q}}-{{B}_{P}}\]  \[=\frac{{{\mu }_{0}}}{4\pi }\cdot \frac{2}{r}({{i}_{Q}}-{{i}_{P}})\]  \[=\frac{{{\mu }_{0}}}{4\pi }\times \frac{2}{2.5}(5-2.5)=\frac{{{\mu }_{0}}}{2\pi }\]