A) \[\frac{R}{\sqrt{3}}\]
B) \[R\sqrt{3}\]
C) \[2\sqrt{3}\,R\]
D) \[\frac{2}{\sqrt{3}}R\]
Correct Answer: B
Solution :
\[\frac{{{B}_{centre}}}{{{B}_{axis}}}={{\left( 1+\frac{{{x}^{2}}}{{{R}^{2}}} \right)}^{3/2}},\]also \[{{B}_{axis}}=\frac{1}{8}{{B}_{centre}}\] \[\Rightarrow \frac{8}{1}={{\left( 1+\frac{{{x}^{2}}}{{{R}^{2}}} \right)}^{3/2}}\Rightarrow 2={{\left( 1+\frac{{{x}^{2}}}{{{R}^{2}}} \right)}^{1/2}}\] \[\Rightarrow 4=1+\frac{{{x}^{2}}}{{{R}^{2}}}\Rightarrow 3=\frac{{{x}^{2}}}{{{R}^{2}}}\Rightarrow {{x}^{2}}=3{{R}^{2}}\]\[\Rightarrow x=\sqrt{3}R\]
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