Question

The line integral of the vector potential A around the boundary of a surface S represents

• A. flux through the surface S
• B. flux density in the surface S
• C. magnetic density
• D. current density

Answer 1

The correct option is A flux through the surface S

Ans : (a)

Using Stokes's theorem,
$\oint \overrightarrow{A}.\overrightarrow{dL}={\int }_S(▽\times \overrightarrow{A}).d\overrightarrow{S}$
$\because \overrightarrow{A}$ is vector magnetic potential
$\Rightarrow ▽\times \overrightarrow{A}=curl\left(\overrightarrow{A}\right)$
= Magnetic flux density $\overrightarrow{B}$
$\Rightarrow {\int }_s(▽\times \overrightarrow{A}).d\overrightarrow{S}={\int }_s\overrightarrow{B}.d\overrightarrow{S}$
=flux through the surface S.