question_answer

Two straight and long conductors AOB and COD are perpendicular to each other and carry currents of \[{{I}_{1}}\,\,and\,\,{{I}_{2}}\]. The magnitude of the  magnetic field at a point P at a distance a from point O in a direction perpendicular to the plane ABCD is-

A) \[\frac{{{\mu }_{0}}}{2\pi a}({{I}_{1}}+{{I}_{2}})\]               

B) \[\frac{{{\mu }_{0}}}{2\pi a}({{I}_{1}}-{{I}_{2}})\]

C) \[\frac{{{\mu }_{0}}}{2\pi a}{{(I_{1}^{2}-I_{2}^{2})}^{1/2}}\]       

D) \[\frac{{{\mu }_{0}}}{2\pi a}\frac{{{I}_{1}}{{I}_{2}}}{({{I}_{1}}+{{I}_{2}})}\]

Correct Answer: C

Solution :

\[{{B}_{1}}\,\,=\,\,\frac{{{\mu }_{0}}{{I}_{1}}}{2\pi d}\] \[{{B}_{2}}\,\,=\,\,\frac{{{\mu }_{0}}{{I}_{2}}}{2\pi d}\] \[B=\sqrt{B_{1}^{2}+B_{2}^{2}}\]