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Current ‘i’ is flowing in hexagonal coil of side a. The magnetic induction at the centre of the coil will be

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a

$\frac{μ_{0} i}{\sqrt{3} π a}$

b

$\frac{3 \sqrt{3} μ_{0} i}{π a}$

c

$\frac{\sqrt{3} μ_{0} i}{π a}$

d

$\frac{μ_{0} i}{3 \sqrt{3} π a}$

answer is D.

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Detailed Solution

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$∵ B = \frac{μ_{0} i}{4 πr} (\sin θ_{1} + \sin θ_{2}); B_{Net} = 6 B B_{net} = \frac{6 \times μ_{0} i (\frac{1}{2} + \frac{1}{2})}{4 π (\frac{a \sqrt{3}}{2})} = \frac{\sqrt{3} μ_{0} i}{πa} (\begin{array}{l} ∵ θ_{1} = θ_{2} = 30^{0} \\ r = \frac{\sqrt{3} a}{2} \end{array})$

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