Two identical current carrying co-axial loops, carry current i in an opposite sense. A simple amperian loop passes through both of them. Calling the loop as C,

Consider a simple amperian loop passing once through both the identical current carrying coaxial loop.

(i) According to Amper's circuital law.

${\text{∮}}_{\mathrm{C}}\mathrm{B}\cdot \mathrm{dl}={\mathrm{\mu }}_0(\mathrm{l}-\mathrm{l})=0$

(ii) As ${\text{∮}}_{\mathrm{C}}\mathrm{B}\cdot \mathrm{dl}=0,\text{ therefore }{\text{∮}}_{\mathrm{C}}\mathrm{B}\cdot \mathrm{dl}\text{ is }$independent of sense of C
(iii)The shape of C can be arbitrarily chosen.

(iv) The value of B does not vanish on various points of C.