$$\require{cancel}$$

# 6.10: Flux

• • Contributed by Jeremy Tatum
• Emeritus Professor (Physics & Astronomy) at University of Victoria

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