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A wire bent in the form of a regular polygon of n sides, is inscribed in a circle of radius a. If I ampere is the current flowing in the wire, then the magnetic flux density (magnetic field) at the centre of the circle is

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$\frac{μ_{0} i}{2 πa} \tan (\frac{π}{n})$

$\frac{ni}{2 a} μ_{0} \tan (\frac{π}{n})$

$\frac{μ_{0} ni}{2 πa} \tan (\frac{π}{n})$

$\frac{2}{π} \frac{ni}{a} μ_{0} \tan (\frac{π}{n})$

answer is B.

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Detailed Solution

$\begin{array}{l} r = acos \frac{π}{n} \\ B = n [\frac{μ_{0}}{4 π} \cdot \frac{i}{acos π / n} (\sin \frac{π}{n} + \sin \frac{π}{n})] \\ = \frac{μ_{0} ni}{2 πa} \tan (\frac{π}{n}) \end{array}$

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