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6.10: Flux

Last updated

Mar 5, 2022
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- 6.9: The Magnetic Field H
- 6.11: Ampère’s Theorem

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

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

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

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