Question

In a coaxial, straight cable, the central conductor and the outer conductor carry equal currents in opposite direction. Where the magnetic field will be zero ?

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

Answer 1

The correct option is A outside the cable

A coaxial cable consists of a long cylindrical copper wire of radius r1 surrounded by a cylindrical shell of inner radius r2 and outer radius r3 . The wire and the shell carry
equal and opposite currents I uniformly distributed over their volumes.
The magnetic field lines are circles, centered on the symmetry axis of the coaxial cable.
Consider an integration path with r >r3.
The path integral of B along this path is equal to
$\int \overrightarrow{B}.\overrightarrow{dl}=2\pi rB={\mu }_{0}I$
The current enclosed by an integration path with a radius r > r3 is equal to zero (since the current in the wire and in the shell are flowing in opposite directions). The magnetic field in this region is therefore also equal to zero.