Question 55 of 276

A circular loop of radius $R$ is carrying current $iA$. 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 :

A$1:3\sqrt{2}$B$3\sqrt{2}:2$C$2\sqrt{2}:1$D$1:\sqrt{2}$

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Answer: (C) $2\sqrt{2}:1$

The magnitude of magnetic field at the centre of loop is
${B}_{\text{1}}={B}_{\text{centre}}=\dfrac{{\mu }_{^{\circ}}i}{2R}\ldots \left(1\right)$


The magnitude of magnetic field at a point at a distance $x$ from the centre along axis of loop is
${B}_{\text{axis}}=\dfrac{{\mu }_{^{\circ}}i{R}^{2}}{2{\left({R}^{2}+{x}^{2}\right)}^{\dfrac{3}{2}}}$
${B}_{\text{2}}=\dfrac{{\mu }_{^{\circ}}i{R}^{2}}{2\left({2}^{\dfrac{3}{2}}\right){R}^{3}}\ldots \left(2\right)$ $(\text{since}x=R)$
Dividing equation 1 by equation 2, we get
$\dfrac{{B}_{1}}{{B}_{2}}=2\sqrt{2}:1$

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