A) \[\frac{1}{\sqrt{2}}\]
B) \[\sqrt{2}\]
C) \[\frac{1}{2\sqrt{2}}\]
D) \[2\sqrt{2}\]
Correct Answer: D
Solution :
Magnetic field at the centre \[{{B}_{1}}=\frac{{{\mu }_{0}}}{4\pi }\frac{2\pi nI}{a}\] Magnetic field at a distance x from centre \[{{B}_{2}}=\frac{{{\mu }_{0}}}{4\pi }\frac{2\pi nI{{a}^{2}}}{{{({{a}^{2}}+{{x}^{2}})}^{3/2}}}\] at \[x=a\] \[{{B}_{2}}=\frac{{{\mu }_{0}}}{4\pi }\,\frac{2\pi nI}{{{2}^{3/2}}a}\] \[\frac{{{B}_{1}}}{{{B}_{2}}}={{2}^{3/2}}=2\sqrt{2}\]
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