Question

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

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

Answer 1

Answer: (A)

outside the cable

$\overrightarrow{B}=\overrightarrow{B_{outer}}+\overrightarrow{B_{inner}}$

Since the current carried by the outer and and inner are equal and in opposite direction,

magnetic field produced by the cylinders at a point P( distance r from central axis ) is

$\overrightarrow{B_{outer}}=\frac{{\mu }_0}{4\pi }i\frac{\overrightarrow{dl}\times \overrightarrow{r}}{r^3}$

$\overrightarrow{B_{inner}}=-\frac{{\mu }_0}{4\pi }i\frac{\overrightarrow{dl}\times \overrightarrow{r}}{r^3}$

$\therefore \overrightarrow{B}=\overrightarrow{B_{outer}}+\overrightarrow{B_{inner}}=0$