Question

If a long hollow copper pipe carries a direct current $I$ along length of pipe, the magnetic field due to the hollow conductor will exist

• A. Only inside the pipe
• B. Only outside the pipe
• C. Neither inside nor outside the pipe
• D. Both inside the outside the pipe

Answer 1

The correct option is B Only outside the pipe

Using Ampere's circuital law,

$$\oint B\cdot dl={\mu }_0{I}_{enc}$$

For any point inside the hollow conductor, $I_{enc}=0$

$\Rightarrow B_{in}=0$

For any point inside the hollow conductor, assuming an amperian loop the net current enclosed by the loop is zero i.e., $I_{enc}=0$

$\oint B\cdot dl={\mu }_0{I}_{enc}$

$B\oint dl={\mu }_{0}I$

$\Rightarrow B_{out}=\frac{{\mu }_{0}I}{2\pi r}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.