Magnetic field due to a ring having $n$ turns at a distance $x$ on its axis is proportional to (if $r =$ radius of ring)

\frac{r}{(x^{2} + r^{2})}

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\frac{r^{2}}{{(x^{2} + r^{2})}^{3 / 2}}

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\frac{n r^{2}}{{(x^{2} + r^{2})}^{3 / 2}}

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\frac{n^{2} r^{2}}{{(x^{2} + r^{2})}^{3 / 2}}

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Solution

The correct option is B $\frac{n r^{2}}{{(x^{2} + r^{2})}^{3 / 2}}$
Magnetic field on the axis of circular current carrying wire:

$B = \frac{μ_{0}}{4 π} . \frac{2 π n i r^{2}}{(x^{2} + r^{2})^{3 / 2}}$

$\Rightarrow B \propto \frac{n r^{2}}{(x^{2} + r^{2})^{3 / 2}}$

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