Q. 244.0( 3 Votes )

A polygon of n equal sides is formed by bending a current carrying wire to total length 2πr which carries a current i.

(a) Find the magnetic field B at the center of the n-sided polygon.

(b) By letting n , derive the expression for the induced magnetic field at the center of a circular current carrying wire.

Answer :



a) Using the diagram,


For a polygon of n equal sides, the angle at the centre is .




Considering angle to be very small



Using Biot–Savart’s law for one side of the n-sided polygon,




(substituting the value of r)


(substituting the value of l)


For n-sided polygon


B’ =nB



b) When n , polygon tends to a circle with radius r and magnetic field will tend toward



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