Two identical current carrying coaxial loops, carry current I in an opposite sense. A simple Amperian loop passes through both of them once. Calling the loop as C,

In the given case we will use the ampere’s law i.e. …(i) where,

is magnetic field vector,

is Amperian loop,

is magnetic permeability in vacuum,

I is current inside the Amperian loop;

Now, in the given loop two identical current is flowing but in opposite sense so I inside the Amperian loop sums up to be zero. So, the (a) option is wrong. And in equation RHS is zero so, the is independent of the sense of C.

And, since so there may be a point on C where B and dl are perpendicular.

Since so we can’t comment on only B as the dot product of B and dl is zero which includes the case of being both perpendicular to each other.

Hence, our answers are option (b) and (c).