A circular coil of radius 2R is carrying current ‘i’. The ratio of magnetic fields at the centre of the coil and at a point at a distance 6R from the centre of the coil on the axis of the coil is,

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$10 \sqrt{10}$

$20 \sqrt{5}$

$20 \sqrt{10}$

answer is B.

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Detailed Solution

Magnetic field at the centre of the coil
$B_{1} = \frac{μ_{0} i}{2 (2 R)} = \frac{μ_{0} i}{4 R}$
Magnetic field at a point at a distance ‘6R’ along the axis of the coil
$B_{2} = \frac{μ_{0} i (2 R)^{2}}{2 {[(6 R)^{2} + (2 R)^{2})]}^{3 / 2}} ∴ \frac{B_{1}}{B_{2}} = 10 \sqrt{10}$

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