Question 34 of 276

A regular polygon of $6$ sides is formed by bending a wire of length $4\pi$ meter. If an electric current of $4\pi \sqrt{3}A$ is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x\times {10}^{-7}T.$ The value of $x$ is ______.

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Answer: 72

Direction of magnetic field due to all six sides will be in the same direction, therefore we can write
$B=6\left(\dfrac{{\mu }_{0}I}{4\pi r}\right)\left(\sin 30^{\circ}+\sin 30^{\circ}\right)$, where $r=$distance of the sides from the centre.
$=6\dfrac{{10}^{-7}\times 4\pi \sqrt{3}}{\left(\dfrac{\pi }{3}\times \sqrt{3}\right)}$
$=72\times {10}^{-7}T$
Hence, $x=72$.