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Magnetic Flux Lines
Linked via "magnetic flux density vector"
Flux Linkage and $\Phi$ Notation
The total magnetic flux ($\Phi$) passing through a specified surface $S$ is calculated by integrating the dot product of the magnetic flux density vector ($\mathbf{B}$) and the differential area vector ($d\mathbf{A}$):
$$\Phi = \iint_S \mathbf{B} \cdot d\mathbf{A}$$