Magnetic field due to a ring having $n$ turns at a distance $x$ on its axis is proportional to (if $r$ = radius of ring)
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(c) Magnetic field on the axis of circular current
$B = \frac{{{\mu _0}}}{{4\pi }} \cdot \frac{{2\pi ni{r^2}}}{{{{({x^2} + {r^2})}^{3/2}}}}$ $==>$ $B \propto \frac{{n{r^2}}}{{{{({x^2} + {r^2})}^{3/2}}}}$
$B = \frac{{{\mu _0}}}{{4\pi }} \cdot \frac{{2\pi ni{r^2}}}{{{{({x^2} + {r^2})}^{3/2}}}}$ $==>$ $B \propto \frac{{n{r^2}}}{{{{({x^2} + {r^2})}^{3/2}}}}$
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