A) \[\frac{{{\mu }_{0}}I}{4\pi R}\]
B) \[\frac{{{\mu }_{0}}I}{{{\pi }^{2}}R}\]
C) \[\frac{{{\mu }_{0}}I}{2{{\pi }^{2}}R}\]
D) \[\frac{{{\mu }_{0}}I}{2\pi R}\]
Correct Answer: B
Solution :
[b] |
\[B=\int{dB\sin \theta }\] |
\[B=\int{\frac{{{\mu }_{0}}di}{2\pi R}\sin \theta }\] |
\[=\frac{{{\mu }_{0}}}{2\pi R}\left( \frac{i}{\pi R} \right)R\int\limits_{0}^{\pi }{\sin \theta d\theta }\] |
\[=\frac{{{\mu }_{0}}i}{{{\pi }^{2}}R}\] |
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