Question

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

• 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

The direction of current in central and outer conductor is opposite. hence using Ampere's circular law:


So, $i_1=i_2$

Using Ampere’s circuital law

$\oint \overrightarrow{B}.\overrightarrow{dl}={\mu }_0\left(I_{enclosed}\right)$

So, applying this law on outer loop given in figure

$\oint \overrightarrow{B}.\overrightarrow{dl}={\mu }_0\left(I_{enclosed}\right)={\mu }_0(i_1-i_2)=0$

The net magnetic field can only be zero outside cable, since the term $I_{\text{enclosed}}$ could become zero.

Thus, option $\left(a\right)$ is correct.