A cell is connected between the points $A$ and $C$ of a circular conductor $ABCD$ of centre $O$ with angle $AOC = {60^o}$. If ${B_1}$ and ${B_2}$ are the magnitudes of the magnetic fields at $O$ due to the currents in $ABC$ and $ADC$ respectively, the ratio $\frac{{{B_1}}}{{{B_2}}}$ is
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$B = \frac{{{\mu _0}}}{{4\pi }}\frac{{\theta \,i}}{r} \Rightarrow B \propto \theta \,i$ ($\frac{{{i_1}}}{{{i_2}}} = \frac{{{l_2}}}{{{l_1}}} = \frac{{{\theta _2}}}{{{\theta _1}}}$)
$ \Rightarrow \frac{{{B_1}}}{{{B_2}}} = \frac{{{\theta _1}}}{{{\theta _2}}}.\frac{{{i_1}}}{{{i_2}}}$
$\frac{{{B_1}}}{{{B_2}}} = \frac{{{\theta _1}}}{{{\theta _2}}} \times \frac{{{\theta _2}}}{{{\theta _1}}}$
$ \Rightarrow {B_1} = {B_2}$
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