Question

A coaxial cable consists of a thin inner conductor fixed along the axis of a hollow outer conductor. The two conductors carry equal currents in opposite directions. Let $B_1$ and $B_2$ be the magnetic fields in the region between the conductors and outside the hollow conductor respectively. Then:

• A. $B_1\ne 0,B_2\ne 0$
• B. $B_1=B_2=0$
• C. $B_1\ne 0,B_2=0$
• D. $B_1=0,B_2\ne 0$

Answer 1

The correct option is C $B_1\ne 0,B_2=0$

Apply Ampere's circuital law to the coaxial circular loops $L_1$ and $L_2$. The magnetic field is $B_1$ at all points on $L_1$ and $B_2$ at all points on $L_2$. $\sum I\ne 0$ for $L_1$ and $0$ for $L_2$. Hence, $B_1\ne 0$ but $B_2=0$.
$[As\oint \overrightarrow{B}\cdot d\overrightarrow{l}={\mu }_0\sum I]$