a
(a) In the following figure, magnetic fields at \(O\) due to sections \(1\), \(2\), \(3\) and \(4\) are considered as \({B_1},\,{B_2},\,{B_3}\) and \({B_4}\) respectively.
\({B_1} = {B_3} = 0\)
\({B_2} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{\pi \,i}}{{{R_1}}} \otimes \)
\({B_4} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{\pi \,i}}{{{R_2}}} \odot\) As \(|{B_2}|\,\, > \,\,|{B_4}|\)
So \({B_{net}} = {B_2} - {B_4} \Rightarrow {B_{net}} = \frac{{{\mu _0}i}}{4}\left( {\frac{1}{{{R_1}}} - \frac{1}{{{R_2}}}} \right) \otimes \)