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

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TestHub · Accepted Answer

The magnitude of magnetic field at the centre of loop is

$B_{1} = B_{centre} = \frac{μ_{\circ} i}{2 R} \dots (1)$

The magnitude of magnetic field at a point at a distance $x$ from the centre along axis of loop is

$B_{axis} = \frac{μ_{\circ} i R^{2}}{2 {(R^{2} + x^{2})}^{\frac{3}{2}}}$

$B_{2} = \frac{μ_{\circ} i R^{2}}{2 (2^{\frac{3}{2}}) R^{3}} \dots (2)$ $(since x = R)$

Dividing equation 1 by equation 2, we get

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

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