
The potential difference across AB is
VA−VB=B1a.V.
⇒2π(x−2a)μiaV
The potential difference across CD is
VC−VD=B2a.V
B2=2π(x+2a)μ0i
VC−VD=2π(x+2a)μ0iaV
Net Potential difference =2πμiaV(x−2a1−x+2a1)
(VA−VB)−(VC−VD)=2πμia(x2−4a22a)∝4x2−a21∝(2x+a)(2x−a)1