6.10: Flux
- Page ID
- 5746
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 |