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A regular polygon of 'n sides is formed by bending a wire of length 2 pi R which carries a current i. Find the magnetic field at the centre of the polygon? |
Answer» SOLUTION : ONE side of polygon `a = (2pir)/(n)` `alpha = beta = ((2pi)/(n))//2 = (PI)/(n) , cot alpha = (d)/(a//2)` ` d = (a)/(2) cot alpha = (pi R)/(n) cot"" ((pi)/(n))` All SIDES of polygen produce magnetic FIELD at O in same direction. so,, B = n (magnetic field due to one side) ` = n (mu_0i)/(4pi)(n)/(pi R cot ""(pi)/(n))(sin ""pi/n + sin "" pi/n)` `= (mu_0i)/(4R) (n^2)/(pi^2)(2 sin pi//n)/(cos pi//n) . sin ""pi/n` `B = (mu_0i)/(2R) xx ({sin pi//n//_(pi//n)}^2)/(cos pi//n)` |
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