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,

Options

A. `underset(C)oint vecB * dvecl = m_(0)I`.
B. the value of `underset(C )oint vec B * d vecl` is independent of sense of C.
C. there may be a point on C where `vec B` and `d vecl` are perpendicular.
D. `vec B` vanishes everywhere on C.

Answer

b, c

Explanation

Let us consider an Amperian loop passing once through the identical current carrying loops. If I is the current passing through each loop, then according to Ampère.s circuital law, we have:
`underset(C ) o int vec B * vec (dl) = mu_(0) (I - I) = 0 ` [Current flowing in loops are in opposite directions ]
So , `underset (C ) o int vec B * vec (dl) ` is independent of the sense of C .
If suppose plane of the Amperian loop is kept perpendicular to the plane of the coils then magnetic field, being along the axis of coils, must become perpendicular to the loop at some point. Hence there can be a point on C, lying on the axis of two coaxial loops, where `vec B " and " vec (dl)` are perpendicular.
Therefore, optiona (b) and (c) are correct.