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	ML^3T^-2Q^-1
$\Phi_D$	C	Q
$\Phi_B$	Wb	ML^2T^-1Q^-1
$\Phi_H$	A m	LT^-1Q