A) \[\frac{{{\mu }_{0}}i}{r}({{r}_{1}}+{{r}_{2}})\]
B) \[\frac{{{\mu }_{0}}i}{4}({{r}_{1}}-{{r}_{2}})\]
C) \[\frac{{{\mu }_{0}}i}{4}\left( \frac{{{r}_{1}}+{{r}_{2}}}{{{r}_{1}}{{r}_{2}}} \right)\]
D) \[\frac{{{\mu }_{0}}i}{4}\left( \frac{{{r}_{2}}-{{r}_{1}}}{{{r}_{1}}{{r}_{2}}} \right)\]
Correct Answer: C
Solution :
The magnetic induction due to both semicircular parts will be in the same direction perpendicular to the paper inwards. \[\therefore B={{B}_{1}}+{{B}_{2}}=\frac{{{\mu }_{0}}i}{4{{r}_{1}}}+\frac{{{\mu }_{0}}i}{4{{r}_{2}}}=\frac{{{\mu }_{0}}i}{4}\left( \frac{{{r}_{1}}+{{r}_{2}}}{{{r}_{1}}{{r}_{2}}} \right)\otimes \]
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