question_answer

Two very long, straight, and insulated wires are kept at \[90{}^\circ \] angle from each other in xy-plane as shown in the figure. These wires carry currents of equal magnitude I, whose directions are shown in the figure. The net magnetic field at point P will be :                     [JEE Main 8-4-2019 Afternoon]

A) Zero    

B) \[\frac{+{{\mu }_{0}}I}{\pi d}(\hat{z})\]

C) \[-\frac{{{\mu }_{0}}I}{2\pi d}(\hat{x}+\hat{y})\]

D)   \[\frac{{{\mu }_{0}}I}{2\pi d}(\hat{x}+\hat{y})\]

Correct Answer: A

Solution :

Magnetic field at point P \[{{\vec{B}}_{net}}=\frac{{{\mu }_{0}}I}{2\pi d}\left( -\hat{k} \right)+\frac{{{\mu }_{0}}I}{2\pi d}\left( {\hat{k}} \right)=0\]