# 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^{-2}Q^{-1} |

\(\textbf{D}\) | C m^{-2} | L^{-2}Q |

\(\textbf{B}\) | T | MT^{-1}Q^{-1} |

\(\textbf{H}\) | A m^{-1} | L^{-1}T^{-1}Q |

\(\Phi_E\) | V m | ML^{3}T^{-2}Q^{-1} |

\(\Phi_D\) | C | Q |

\(\Phi_B\) | Wb | ML^{2}T^{-1}Q^{-1} |

\(\Phi_H\) | A m | LT^{-1}Q |