A regular polygon of $6$ sides is formed by bending
a wire of length $4 \pi$ meter. If an electric current of $4 \pi \sqrt{3} \mathrm{~A}$ is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x \times 10^{7} \mathrm{~T}$. The value of $\mathrm{x}$ is______.
JEE MAIN 2024, Diffcult
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$\frac{4 \pi}{6} \mathrm{~m}$
$B=6\left(\frac{\mu_0 I}{4 \pi r}\right)\left(\sin 30^{\circ}+\sin 30^{\circ}\right)$
$= 6 \frac{10^{-7} \times 4 \pi \sqrt{3}}{\left(\frac{\sqrt{3} \times 4 \pi}{2 \times 6}\right)}$
$=72 \times 10^{-7} \mathrm{~T}$
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