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

Contributor

• Jeremy Tatum (University of Victoria, Canada)