The magnetic field at the center of current carrying circular loop is B₁. The magnetic field at a distance of $\sqrt{3}$ times radius of the given circular loop from the center on its axis is B₂. The value of B₁/B₂ will be

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8 : 1

12 : $\sqrt{5}$

9 : 4

5 : $\sqrt{3}$

answer is C.

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Detailed Solution

$B_{1} = \frac{μ_{0} I}{2 R} B_{2} = \frac{μ_{0} {IR}^{2}}{2 {(R^{2} + 3 R^{2})}^{3 / 2}} = \frac{1}{8} (\frac{μ_{0} I}{2 R}) = \frac{B_{1}}{8} \frac{B_{1}}{B_{2}} = \frac{8}{1}$

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