91Ó°ÊÓ

• Figure showing four circular Amperian loops.
• The current is uniform across the wire’s circular cross-section.

Using Ampere’s law, rank theloops according to the magnitude ofaround each.

The formula is as follows:

$\mathbf{âˆ\circledR }\stackrel{\mathbf{→}}{\mathit{B}}\mathbf{.}\stackrel{\mathbf{→}}{\mathit{d}\mathit{s}}\mathbf{=}{\mathit{μ}}_{\mathbf{0}}{\mathit{i}}_{\mathbf{e}\mathbf{n}\mathbf{c}}$

Where, $\stackrel{\mathbf{→}}{\mathbf{B}}$is the magnetic field,

$\stackrel{\mathbf{→}}{\mathit{d}\mathit{s}}$is the infinitesimal segment of the integration path,

${\mathit{μ}}_{\mathbf{0}}$is the empty's permeability,
localid="1662742639512" ${\mathit{i}}_{\mathbf{enc}}$is the enclosed electric current by the path.

According to Ampere’s law,

$\mathbf{âˆ\circledR }\stackrel{\mathbf{→}}{\mathit{B}}\mathbf{.}\stackrel{\mathbf{→}}{\mathit{d}\mathit{s}}\mathbf{=}{\mathit{μ}}_{\mathbf{0}}{\mathit{i}}_{\mathbf{enc}}$

From the given figure, it can interpret that,

$i_{enc,c}=i_{enc,d}$

Also,

$i_{enc,b}>i_{enc,a}$

And,

$i_{enc,c}>i_{enc,b}$

(Since the area enclosed by loop b is greater than that by loop a and the area enclosed by loop c is greater than that by b.)

Hence, the ranking of the loops according to the magnitude ofeach is,$c=0>0>a$

Ampere’s law gives the relation between magnetic flux and current enclosed by the loop.