Page 274 - Engineering Electromagnetics, 8th Edition

256 ENGINEERING ELECTROMAGNETICS

Ohm’s law for the electric circuit has the point form
J = σE (40a)

and we see that the magnetic flux density will be the analog of the current density,

B = µH (40b)

To find the total current, we must integrate:

J · dS (41a)
I =
S
A corresponding operation is necessary to determine the total magnetic flux flowing
through the cross section of a magnetic circuit:

= B · dS (41b)
S
We then defined resistance as the ratio of potential difference and current, or

V = IR (42a)
and we shall now define reluctance as the ratio of the magnetomotive force to the
total flux; thus

V m = (42b)

where reluctance is measured in ampere-turns per weber (A · t/Wb). In resistors that
are made of a linear isotropic homogeneous material of conductivity σ and have a
uniform cross section of area S and length d, the total resistance is
d
R = (43a)
σS
If we are fortunate enough to have such a linear isotropic homogeneous magnetic
material of length d and uniform cross section S, then the total reluctance is

d
= (43b)
µS
The only such material to which we shall commonly apply this relationship is air.
Finally, let us consider the analog of the source voltage in an electric circuit. We
know that the closed line integral of E is zero,

E · dL = 0
In other words, Kirchhoff’s voltage law states that the rise in potential through the
source is exactly equal to the fall in potential through the load. The expression for