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) `B_(centre)=0`
`(mu_0I)/(4pib)odot+(mu_0I)/(4pib)odot +(mu_0I)/(2b)odot +(mu_0I)/(2a)ox=0`
`implies (mu_0I)/(2pib)+(mu_0I)/(2b)-(mu_0I)/(2a)=0 implies 1/(2pib)+1/(2b)=1/(2a)`
`implies a/b=pi/(pi+1)`