In a coaxial, straight cable, the central conductor and the outer… - Vidyadip

MCQ

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

Outside the cable.
Inside the inner conductor.
Inside the outer conductor.
In between the tow conductors.

✓
$A$ and $B$
B
$B$ and $D$
C
$A$ and $D$
D
Only $D$

✓

Answer

Correct option: A.

$A$ and $B$

According to Ampere's law, in a coaxial, straight cable carrying currents $i$ in the inner conductor and $-i$ $($equally in the opposite direction$)$ in the outside conductor.
Inside the inner conductor
$\oint\overrightarrow{\text{B}}.\text{d}\overrightarrow{\text{l}}=\mu_0\text{i}_\text{inside}$
$\oint\overrightarrow{\text{B}}.\text{d}\overrightarrow{\text{l}}=0$
$\Rightarrow\text{b.l}=0$
$\Rightarrow\text{B}=0$
In between the $2$ conductors
$\oint\overrightarrow{\text{B}}.\text{d}\overrightarrow{\text{l}}=\mu_0\text{i}$
$\Rightarrow\text{B}=\frac{\mu_0\text{i}}{2\pi\text{r}}$
Outside the outer conductor
$\oint\overrightarrow{\text{B}}.\text{d}\overrightarrow{\text{l}}=\mu_0\text{i}$
$\Rightarrow\text{B}=0$
Therefore, the magnetic field is zero outside the cable.

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