A wire $A$, bent in the shape of an arc of a circle, carrying a current of $2\, A$ and having radius $2\, cm$ and another wire $B ,$ also bent in the shape of arc of a circle, carrying a current of $3\, A$ and having radius of $4\, cm ,$ are placed as shown in the figure. The ratio of the magnetic fields due to the wires $A$ and $B$ at the common centre $O$ is
JEE MAIN 2020, Diffcult
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Given $i_{A}=2, r_{A}=2 cm , \theta_{A}=2 \pi-\frac{\pi}{2}=\frac{3 \pi}{2}$
$i_{B}=3, r_{B}=4 cm , \theta_{B}=2 \pi-\frac{\pi}{3}=\frac{5 \pi}{3}$
$B=\frac{\mu_{0} I \theta}{4 \pi R}$
$\frac{B_{A}}{B_{B}}=\frac{I_{A}}{I_{B}} \times \frac{\theta_{A} R_{B}}{\theta_{B} R_{A}}=\frac{6}{5}$
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