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6.10: Flux

Recall from Section 1.8 that we defined two extensive scalar quantities for the electric field

\[\Phi_E = \iint \textbf{E}\cdot d\textbf{A}\tag{6.10.1}\]

and

\[\Phi_D = \iint \textbf{D}\cdot d\textbf{A}\tag{6.10.2}\]

which I called the \(E\)-flux and the \(D\)-flux, respectively. In an entirely similar manner I can define the \(B\)-flux and \(H\)-flux of a magnetic field by

\[\Phi_B = \iint \textbf{B}\cdot d\textbf{A}\tag{6.10.3}\]

and

\[\Phi_H = \iint \textbf{H}\cdot d\textbf{A}\tag{6.10.4}\]

The SI unit of \(\Phi_B\) is the tesla metre-squared, or \(\text{T m}^2\), also called the weber Wb. A summary of the SI units and dimensions of the four fields and fluxes might not come amiss here.

\(\textbf{E}\)  V m-1 MLT-2Q-1
\(\textbf{D}\) C m-2 L-2Q
\(\textbf{B}\) T MT-1Q-1
\(\textbf{H}\) A m-1 L-1T-1Q
\(\Phi_E\)  V m ML3T-2Q-1
\(\Phi_D\) C Q
\(\Phi_B\) Wb  ML2T-1Q-1
\(\Phi_H\) A m LT-1Q