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