Question

In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero.

• A. inside the outer conductor
• B. in between the two conductors
• C. outside the cable
• D. inside the inner conductor

Answer 1

Answer: (C)

outside the cable

Answer 2

Consider an Amperian loop outside the coaxial cable (radius $r$ greater than the outer radius of the cable). The current enclosed by this loop is the sum of the current in the central conductor ($I$) and the current in the outer conductor ($-I$, since it's in the opposite direction).

Total current enclosed, $I_{enc} = I + (-I) = 0$.

According to Ampere's Law, $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}$.

Since $I_{enc} = 0$, the magnetic field $B$ outside the cable must be zero. Inside the inner conductor, in between the two conductors, and inside the outer conductor, the net current enclosed would be non-zero, leading to a non-zero magnetic field.