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. `oint vecB.dvecl=+-2mu_0I`
B. the value of `oint_CvecB.dvecl` is independent of sense of C
C. there may be a point on C where `vecB` and `dvecl` are perpendicular
D. `vecB` vanishes everywhere on C

Answer

B, C

Explanation

Consider a simple amperian loop passing once through both the identical current carrying coaxial loops.
(i) According to Ampere circuital law, `oint_CvecB.dvecl=mu_0(I-I)=0`. Hence, option (a) is wrong.
(ii) As `oint_CvecB.dvecl=0`, therefore `oint_CvecB.dvecl` is independent of sense of C. Thus option (b) is correct.
(iii) There will be a point on loop C, lying at the axis of two loops A and B, where `vecB` and `dvecl` are perpendicular to each other. Thus option(c) is correct.
(iv) The value of `vecB` does not vanish on various points of C. Thus option (d) is wrong.