A) \[\frac{{{\mu }_{0}}i}{2\sqrt{2}R}\]
B) \[\frac{{{\mu }_{0}}i}{2R}\]
C) \[\frac{{{\mu }_{0}}i}{4R}\]
D) \[\frac{{{\mu }_{0}}i}{\sqrt{2}R}\]
Correct Answer: A
Solution :
| [a] The magnetic field at centre O for each semicircular parts each of radius R, |
| \[{{B}_{1}}={{B}_{2}}=\frac{{{\mu }_{0}}i}{4R}\] |
| The magnetic field at their common centre |
| \[\overset{\to }{\mathop{\mathbf{B}}}\,=\overset{\to }{\mathop{{{\mathbf{B}}_{1}}}}\,+\overset{\to }{\mathop{{{\mathbf{B}}_{2}}}}\,\] |
| \[B=\sqrt{B_{1}^{2}+B_{2}^{2}}\] |
| \[=\sqrt{{{\left( \frac{{{\mu }_{0}}i}{4R} \right)}^{2}}+{{\left( \frac{{{\mu }_{0}}i}{4R} \right)}^{2}}}\] |
| \[B=\frac{{{\mu }_{0}}i}{2\sqrt{2}R}\] |
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