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.

Options

A. `B=(mu_(0)i)/(4 pi R) sqrt((2pi^(2)-2pi+1))`
B. `B=(mu_(0)i)/(4 pi R) sqrt(2(2pi^(2)-2pi+1))`
C. `B=(mu_(0)i)/(2 pi R) sqrt((2pi^(2)-2pi+1))`
D. None of these

Answer

B

Explanation

`vec(B_A) =(mu_(0)R)/(4 pi R) hat(k) +(mu_(0)I)/(2R) hat(i)-(mu_(0)I)/(4 pi R) hat(j)`
`B_(A) = (mu_(0)I)/(4 pi R) sqrt((2 pi-1)^(2)+(1)^(2)) =(mu_(0)I)/(4 pi R) sqrt(2(2 pi^(2)-2 pi +1))`.