An otherwise infinite, straight wire has two concentric loops of radii a and b carrying equal currents in opposite directions as shown in Fig. The magnetic field at the common centre is zero for

Options

A. `a/b=(pi-1)/(pi)`
B. `a/b=(pi)/(pi+1)`
C. `a/b=(pi-1)/(pi+1)`
D. `a/b=(pi+1)/(pi-1)`

Answer

B

Explanation

`B_(centre)=0`
`(mu_(0)I)/(4pib) o.+(mu_(0)I)/(4pib) o.+(mu_(0)I)/(2b) o.+(mu_(0)I)/(2a) ox=0`
`(mu_(0)I)/(2pib) +(mu_(0)I)/(2b) -(mu_(0)I)/(2a) =0`
`1/(2pib)+1/(2b)=1/(2a)`
`a/b=(pi)/(pi-1)`