A) \[\frac{B}{2}\]
B) \[\frac{B}{4}\]
C) \[\frac{B}{\sqrt{8}}\]
D) \[\sqrt{8}B\]
Correct Answer: C
Solution :
The magnetic field at a point along the axis at distance R from the centre of a circular coil of radius R carrying current i is \[{{B}_{A}}=\frac{{{\mu }_{0}}2\pi i{{R}^{2}}}{4\pi {{({{R}^{2}}+{{R}^{2}})}^{3/2}}}\] \[=\frac{{{\mu }_{0}}i}{2\sqrt{8}R}\] \[=\frac{B}{\sqrt{8}}\]\[\left[ {{B}_{\text{centre}}}=B=\frac{{{\mu }_{0}}i}{2R} \right]\]
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