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6.10: Flux

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

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


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

    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

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


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

    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