Question

Find the magnitude of the magnetic induction B of a magnetic field generated by a system of thin conductors along which a current I is flowing at a point A (O, R, O), that is the centre of a circular conductor of radius R. The ring is in yz plane.

Answer 1

Correct Answer - `B=(mu_(0)i)/(4piR) sqrt(2(2pi^(2) -2pi+1))`
`oversetrarrB_(1) = (mu_(0))/(4pi) (I)/(R) (-hatk) oversetrarrB_(2) = (mu_(0))/(4pi) (2piI)/(R)(hati)`
`oversetrarr(B_(3)) =(mu_(0))/(4pi) (I)/(R) (-hati)`
`oversetrarrB =oversetrarrB_(1)=oversetrarrB_(2)oversetrarrB_(3)`
`=(mu_(0))/(4pi) (I)/(R) (2pi -1) hati + (mu_(0))/(4pi) (I)/(R) (hatk)`
`B =(mu_(0))/(4pi) (I)/(R) sqrt((2pi -1)^(2) +1)`
`=(mu_(0))/(4pi) (I)/(R) sqrt(2 (2pi^(2) - 2pi + 1))`
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