A regular polygon of 6 sides is formed by bending a wire of length 4 π meter. If an electric current of 4 π 3 A is flowing through the sides of the polygon, the magnetic field at the centre of the pol

Question

A regular polygon of 6 sides is formed by bending a wire of length 4 π meter. If an electric current of 4 π 3 A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be x × 10 - 7 T . The value of x is ______.

TestHub · Accepted Answer

Direction of magnetic field due to all six sides will be in the same direction, therefore we can write

$B = 6 (\frac{μ_{0} I}{4 π r}) (\sin 30 ° + \sin 30 °)$ , where $r =$ distance of the sides from the centre.

$= 6 \frac{10^{- 7} \times 4 π \sqrt{3}}{(\frac{π}{3} \times \sqrt{3})}$

$= 72 \times 10^{- 7} T$

Hence, $x = 72$ .

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