A current $i$ in a circular loop of radius $b$ produces magnetic field. At a fixed point far from the loop (on its axis) the magnetic field is proportional to which of the following combinations of $i$ and $b$ ?

i b

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i b^{2}

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i^{2} b

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i / b^{2}

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Solution

The correct option is A $i b^{2}$
The magnetic field on the axis at a distance a from the center of a current carrying circular loop of radius b is,
$B_{a x i s} = \frac{μ_{0} i b^{2}}{(b^{2} + a^{2})^{\frac{3}{2}}}$
Given, $a >> b$
$∴ B_{a x i s} = \frac{μ_{0} i b^{2}}{a^{3} (1 + \frac{a^{2}}{b^{2}})^{\frac{3}{2}}} = \frac{μ_{0} i b^{2}}{a^{3}}$
where we have neglected $\frac{a^{2}}{b^{2}}$ in comparison to 1,
$∴ B_{a x i s} \propto i b^{2}$

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