question_answer

Two straight long conductors AOB and COD are perpendicular to each other and carry currents \[{{\text{I}}_{1}}\] and \[{{\text{I}}_{\text{2}}}\] respectively. The magnitude of the magnetic induction at a point P at a distance 'a' from the point 0 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) \[\frac{{{\mu }_{0}}}{2\pi a}{{\left[ I_{1}^{2}+I_{2}^{2} \right]}^{1/2}}\]

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

Correct Answer: C

Solution :

            \[\overrightarrow{B}\] due to AOB and COD are\[\bot \] to each other. Hence, net\[{{\overrightarrow{B}}^{2}}=B_{1}^{2}+B_{2}^{2}\] \[B=\frac{{{\mu }_{0}}}{2\pi a}{{(1_{1}^{2}+1_{2}^{2})}^{1/2}}\](\[\bot \]to plane ABCD)