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Q.

A circular loop of radius r is carrying current $I A$ . The ratio of magnetic field at the center of circular loop and at a distance r from the center of the loop on its axis is:

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a

1 : 3 $\sqrt{2}$

b

1 : $\sqrt{2}$

c

3 $\sqrt{2}$ : 2

d

2 $\sqrt{2}$ : 1

answer is B.

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Detailed Solution

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At centre, $B_{1} = \frac{μ_{0} i}{2 r}$
On the axis, $B_{2} = \frac{μ_{0} {ir}^{2}}{2 {(r^{2} + r^{2})}^{3 / 2}} = \frac{μ_{0} {ir}^{2}}{2 \times 2 \sqrt{2} \cdot r^{3}}$
$\begin{array}{l} = \frac{μ_{0} i}{2 \times 2 \sqrt{2} r} \\ ∴ B_{1} : B_{2} = 2 \sqrt{2} : 1 \end{array}$

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