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Arrange the following in ascending order of magnetic induction at a point on axis of circular loop of radius (r) at a distance (x) from its centre (for the same currents in the loops)
a) $r = R; x = \sqrt{3} R$
b) $r = 2 R; x = \sqrt{5} R$
c) $r = \frac{R}{2}; x = 2 \sqrt{2} R$

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a, c, b

a, b, c

b, c, a

c, a, b

answer is D.

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Detailed Solution

$B = \frac{μ_{0} {ir}^{2}}{2 {(r^{2} + x^{2})}^{3 / 2}}$

a) $B = \frac{μ_{0} {iR}^{2}}{2 {(R^{2} + 3 R^{2})}^{3 / 2}} = \frac{μ_{0} i}{16 R}$

b) $B = \frac{μ_{0} i (4 R^{2})}{2 {(4 R^{2} + 5 R^{2})}^{3 / 2}} = \frac{2 μ_{0} i}{27 R}$

c) $B = \frac{μ_{0} i (R^{2} / 4)}{2 {[(R^{2} / 4) + 8 R^{2}]}^{3 / 2}} = \frac{μ_{0} i}{33 \sqrt{33} R}$

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