A circular loop of radius is carrying current 1 A. The ratio of magnetic field at the center of the circular loop and at a distance from the center of the loop on its axis is [2023]

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Solution

Q.
A circular loop of radius $r$ is carrying current 1 A. The ratio of magnetic field at the center of the circular loop and at a distance $r$ from the center of the loop on its axis is [2023]

1 $1 : 3 \sqrt{2}$

2 $2 \sqrt{2} : 1$

3 $3 \sqrt{2} : 2$

4 $1 : \sqrt{2}$

Ans.
(2)

Magnetic field due to a current carrying circular loop on its axis is given as

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

$At centre, x = 0, B_{1} = \frac{μ_{0} i}{2 r}$

$At x = r, B_{2} = \frac{μ_{0} i}{2 \times 2 \sqrt{2} r}$

$\Rightarrow \frac{B_{1}}{B_{2}} = 2 \sqrt{2}$

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