d
(d) Magnetic field at \(P\) due to wire \(1\), \({B_1} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\,(8)}}{d}\)
and due to wire \(2\), \({B_2} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\,(6)}}{d}\)
\(==>\) \({B_{net}} = \sqrt {B_1^2 + B_2^2} = \sqrt {{{\left( {\frac{{{\mu _0}}}{{4\pi }}.\frac{{16}}{d}} \right)}^2} + {{\left( {\frac{{{\mu _0}}}{{4\pi }}.\frac{{12}}{d}} \right)}^2}} \)
\( = \frac{{{\mu _0}}}{{4\pi }} \times \frac{2}{d} \times 10 = \frac{{5{\mu _0}}}{{\pi d}}\)