Two straight long conductors $AOB$ and $COD$ are perpendicular to each other and carry currents ${i_1}$ and ${i_2}$. The magnitude of the magnetic induction at a point $ P$ at a distance a from the point $O$ in a direction perpendicular to the plane $ACBD$ is
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(c) At $P$ : ${B_{net}} = \sqrt {B_1^2 + B_2^2} $
$ = \sqrt {{{\left( {\frac{{{\mu _0}}}{{4\pi }}\frac{{2{i_1}}}{a}} \right)}^2} + {{\left( {\frac{{{\mu _0}}}{{4\pi }}\frac{{2{i_2}}}{a}} \right)}^2}} $
$ = \frac{{{\mu _0}}}{{2\pi a}}{(i_1^2 + i_2^2)^{1/2}}$
$ = \sqrt {{{\left( {\frac{{{\mu _0}}}{{4\pi }}\frac{{2{i_1}}}{a}} \right)}^2} + {{\left( {\frac{{{\mu _0}}}{{4\pi }}\frac{{2{i_2}}}{a}} \right)}^2}} $
$ = \frac{{{\mu _0}}}{{2\pi a}}{(i_1^2 + i_2^2)^{1/2}}$
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