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(D) The given situation is shown in the figure. $A$ regular hexagon consists of $6$ identical straight wire segments.First,we calculate the magnetic f

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$\frac{\sqrt{3} \mu_0 I}{\pi R}$

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(D) The given situation is shown in the figure. $A$ regular hexagon consists of $6$ identical straight wire segments.First,we calculate the magnetic field at the centre $O$ due to one current segment $AB$.In $	riangle OAM$,the perpendicular distance $r$ from the centre $O$ to the segment $AB$ is $OM$.Since the hexagon is regular,$	riangle OAB$ is an equilateral triangle with sides $R$. Thus,$OM = R \sin 60^{\circ} = \frac{\sqrt{3}}{2} R$.The magnetic field $B_1$ at point $O$ due to segment $AB$ is given by the formula $B = \frac{\mu_0 I}{4 \pi r} (\sin 	heta_1 + \sin 	heta_2)$.Here,$	heta_1 = 	heta_2 = 30^{\circ}$.$B_1 = \frac{\mu_0 I}{4 \pi (\frac{\sqrt{3}}{2} R)} (\sin 30^{\circ} + \sin 30^{\circ}) = \frac{\mu_0 I}{2 \sqrt{3} \pi R} (\frac{1}{2} + \frac{1}{2}) = \frac{\mu_0 I}{2 \sqrt{3} \pi R}$.The total magnetic field $B$ at the centre is the sum of the fields due to all $6$ segments:$B = 6 	imes B_1 = 6 	imes \frac{\mu_0 I}{2 \sqrt{3} \pi R} = \frac{3 \mu_0 I}{\sqrt{3} \pi R} = \frac{\sqrt{3} \mu_0 I}{\pi R}$.

$A$ conducting wire is in the shape of a regular hexagon which is inscribed inside an imaginary circle of radius $R$. If a current $I$ flows through the wire,the magnitude of the magnetic field at the centre of the circle is

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