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Q.

A current ‘i’ flows through a thin wire shaped as regular polygon of  ‘n’ sides which can be inscribed in a circle of radius R. The magnetic field induction at the centre of polygon due to one side of the polygon is

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a

μ0iπRtanπn

b

μ0i4πRtanπn

c

μ0i2πRtanπn

d

μ0i2πRcosπn

answer is C.

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Detailed Solution

B=μ0I4πrsinπn+sinπn But cosπ/n=rR or  r=Rcosπ/n∴ B=μ0I4πRcosπ/n2sinπ/n  ⇒B=μ0I2πRtanπ/n
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