Two circular coils X and Y, having equal numb | vedclass

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Question

(c) Magnetic field at $O$ due to bigger coil $Y$, is
${B_Y} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\pi i{{(2r)}^2}}}{{{{\{ {d^2} + {{(2r)}^2}\} }^{3/2}

Vedclass · Accepted Answer

$\frac{{{B_Y}}}{{{B_X}}} = \frac{1}{2}$

Vedclass · Answer

(c) Magnetic field at $O$ due to bigger coil $Y$, is
${B_Y} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\pi i{{(2r)}^2}}}{{{{\{ {d^2} + {{(2r)}^2}\} }^{3/2}}}} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{8\pi i{r^2}}}{{{{({d^2} + 4{r^2})}^{3/2}}}}$
Magnetic field at $O$ due to smaller coil $X$ is
${B_X} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\pi i{r^2}}}{{{{\left\{ {{{\left( {\frac{d}{2}} \right)}^2} + {r^2}} \right\}}^{3/2}}}} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{16\pi i{r^2}}}{{{{({d^2} + 4{r^2})}^{3/2}}}}$
$==>$ $\;\frac{{{B_Y}}}{{{B_X}}} = \frac{1}{2}$

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