A circular loop of radius R is carrying current iA . The ratio of...

The magnitude of magnetic field at the centre of loop is

${B}_{\text{1}} = {B}_{\text{centre}} = \dfrac{{\mu}_{∘}i}{2R} \ldots \left(1\right)$

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

${B}_{\text{axis}} = \dfrac{{\mu}_{∘}i{R}^{2}}{2{\left({R}^{2} + {x}^{2}\right)}^{\dfrac{3}{2}}}$

${B}_{\text{2}} = \dfrac{{\mu}_{∘}i{R}^{2}}{2\left(2\dfrac{3}{2}\right){R}^{3}} \ldots \left(2\right)$( \text{since}x = R )$</p><p>Dividing equation 1 by equation 2, we get</p><p>$\dfrac{{B}_{1}}{{B}_{2}} = 2\sqrt{2}: 1$