Question

A cylindrical wire of radius R is carrying current i uniformly distributed over its cross-section. If a circular loop of radius 'r' is taken as an amperian loop, then the variation of $\oint \overrightarrow{B}.\overrightarrow{dl}$ (along y-axis) over this loop, with radius ' r’ of loop will be best represented by:

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$\oint \overrightarrow{B}.\overrightarrow{dl}={\mu }_0\left(i_{in}\right)$
For $r\le R$
$i_{in}=\left(\frac{i}{\pi R^2}\right)\left(\pi r^2\right)=\frac{i{r}^2}{R^2}\therefore \oint \overrightarrow{B}.\overrightarrow{dl}=\frac{{\mu }_{o}i{r}^2}{R^2}\propto r^2$
For $r\ge R$
$i_{in}=i=$constante
$\therefore \oint \overrightarrow{B}.\overrightarrow{dl}={\mu }_{0}i=constant$