You know two things about a vector field (mathbf{F}) : (i) (mathbf{F}) has a vector potential (mathbf{A})

Question:

You know two things about a vector field $\mathbf{F}$ :
(i) $\mathbf{F}$ has a vector potential $\mathbf{A}$ (but $\mathbf{A}$ is unknown).
(ii) The circulation of $\mathbf{A}$ around the unit circle (oriented counterclockwise) is 25 .
Determine the flux of $\mathbf{F}$ through the surface $\mathcal{S}$ in Figure 22, oriented with an upward-pointing normal.

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