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`
`implies(mu_(0)I)/(4pib)o.+(mu_(0)I)/(4pib)o.+(mu_(0)I)/(2b)o.+(mu_(0)I)/(2a)o+=0`
`=(mu_(0)I)/(2pib)+(mu_(0)I)/(2b)+(mu_(0)I)/(2a)=0`
`implies(1)/(2pib)+(1)/(2b)=(1)/(2a)`
`implies(1)/(2pib)=(pi)/(pi+1)`