A) \[\frac{{{\mu }_{0}}Ni{{R}^{2}}}{2{{({{R}^{2}}+{{x}^{2}})}^{3/2}}}\]
B) \[\frac{{{\mu }_{0}}Ni}{2R}\]
C) \[\frac{{{\mu }_{0}}Ni{{R}^{2}}}{{{(R+x)}^{2}}}\]
D) zero
Correct Answer: D
Solution :
\[B=\oint{dB\sin \text{o }\!\!|\!\!\text{ }}\] \[B=\frac{{{\mu }_{0}}}{4\pi }\frac{i}{{{r}^{3}}}\int{dt\,\sin \theta }\] \[\sin \text{o }\!\!|\!\!\text{ =}\frac{R}{r}\] \[B=\frac{{{\mu }_{0}}}{4\pi }.\frac{iR}{{{r}^{3}}}\int{dl}\] \[\int{dl}=2\pi R\] and \[r={{({{R}^{2}}+{{x}^{2}})}^{1/2}}\] \[B=\frac{{{\mu }_{0}}}{4\pi }.\frac{2\pi i{{R}^{2}}}{{{({{R}^{2}}+{{x}^{2}})}^{3/2}}}\] \[=\frac{{{\mu }_{0}}i{{R}^{2}}}{2{{({{R}^{2}}+{{x}^{2}})}^{3x}}}\] \[B=\frac{{{\mu }_{0}}Ni{{R}^{2}}}{2{{({{R}^{2}}+{{x}^{2}})}^{3/2}}}\]
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