In the figure shown there are two semicircles of radii ${r_1}$ and ${r_2}$ in which a current $i$ is flowing. The magnetic induction at the centre $O$ will be
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(c) The magnetic induction due to both semicircular parts will be in the same direction perpendicular to the paper inwards.
$\therefore B = {B_1} + {B_2} = \frac{{{\mu _0}i}}{{4{r_1}}} + \frac{{{\mu _0}i}}{{4{r_2}}} = \frac{{{\mu _0}i}}{4}\left( {\frac{{{r_1} + {r_2}}}{{{r_1}{r_2}}}} \right) \otimes $
$\therefore B = {B_1} + {B_2} = \frac{{{\mu _0}i}}{{4{r_1}}} + \frac{{{\mu _0}i}}{{4{r_2}}} = \frac{{{\mu _0}i}}{4}\left( {\frac{{{r_1} + {r_2}}}{{{r_1}{r_2}}}} \right) \otimes $
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