question_answer

    Two infinite long current carrying wires A and B are placed as shown in figure. Each wire carries same current\[I\]. The resultant magnetic field intensity at point P is

A)  \[\frac{{{\mu }_{0}}I}{2\pi a}\]                 

B)  \[\frac{\sqrt{2}{{\mu }_{0}}I}{2\pi a}\]

C)  \[\frac{{{\mu }_{0}}I}{2\sqrt{2}\pi a}\]                 

D)  \[\frac{{{\mu }_{0}}I}{4\sqrt{2}\pi a}\]

Correct Answer: A

Solution :

                \[{{B}_{A}}={{B}_{B}}=\frac{{{\mu }_{0}}I}{2\pi \times \sqrt{2}a}\] So,          \[B=\sqrt{B_{A}^{2}+B_{B}^{2}}=\frac{{{\mu }_{0}}I}{2\pi a}\]