The magnetic induction at the centre $O$ in the figure shown is
IIT 1988, Diffcult
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(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 $
${B_1} = {B_3} = 0$
${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 $
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