11
Coupling of Electromagnetic Fields into Biological Systems
the magnetic field produces an internal electric field that varies directly with distance
away from the center and in proportion to frequency. Note that there is no induced
electric field at the center, but it reaches a maximum at the body surface. For a 60 Hz
uniform magnetic flux density of 0.4 μT (T = Wb/m 2 ) oriented along the long axis of
the human body with 0.12 and 0.20 m as radii of the head and trunk, respectively, the
induced electric fields along the circular path subscribing the head and trunk are 9.04
and 15.07 μV/m, respectively, at the surface.
The electric fields inside circulate in closed loops and form eddy currents in a medium
with finite conductivity σ such that the eddy current density is
J = σE = (σπfrμ)Hϕ
(1.25)
The eddy current’s magnitude increases with distance from the center of the body and
this current encircles the magnetic field that produces it (Figure 1.3)
When applying Equations 1.24 and 1.25 to estimate fields induced or current inside a
biological object (animal, human, or tissue preparation), any significant deviations from
homogeneity or circular symmetry must be taken into account. Equations 1.24 and 1.25
should be applied to each region inside the body having a different conductivity, which
behaves as a unit with its own body center and radius or an equivalent radius. However,
due to the presence of opposing induced field orientations and current paths at internal
interfaces, the highest field and current densities tend to occur with the large dimensions
associated with outer layers of a body or tissue preparation so long as the conductivities
are not grossly different and the regions are not separated by nonconducting materials.
The circulating eddy currents induced inside a prolate homogeneous spheroidal
model of the human body immersed in a uniform horizontal or vertical magnetic field
are shown in Figure 1.3. The induced electric fields are polarization dependent in that
they are always in a plane perpendicular to the magnetic field. The eddy current loop is
the largest when the dimension of the homogeneous region is the largest.
Eddy current
loop
Body model
H field
H field
FigurE 1.3 Circulating eddy currents induced inside a prolate homogeneous model of the
human body immersed in a uniform horizontal or vertical magnetic field.
Coupling of Electromagnetic Fields into Biological Systems
the magnetic field produces an internal electric field that varies directly with distance
away from the center and in proportion to frequency. Note that there is no induced
electric field at the center, but it reaches a maximum at the body surface. For a 60 Hz
uniform magnetic flux density of 0.4 μT (T = Wb/m 2 ) oriented along the long axis of
the human body with 0.12 and 0.20 m as radii of the head and trunk, respectively, the
induced electric fields along the circular path subscribing the head and trunk are 9.04
and 15.07 μV/m, respectively, at the surface.
The electric fields inside circulate in closed loops and form eddy currents in a medium
with finite conductivity σ such that the eddy current density is
J = σE = (σπfrμ)Hϕ
(1.25)
The eddy current’s magnitude increases with distance from the center of the body and
this current encircles the magnetic field that produces it (Figure 1.3)
When applying Equations 1.24 and 1.25 to estimate fields induced or current inside a
biological object (animal, human, or tissue preparation), any significant deviations from
homogeneity or circular symmetry must be taken into account. Equations 1.24 and 1.25
should be applied to each region inside the body having a different conductivity, which
behaves as a unit with its own body center and radius or an equivalent radius. However,
due to the presence of opposing induced field orientations and current paths at internal
interfaces, the highest field and current densities tend to occur with the large dimensions
associated with outer layers of a body or tissue preparation so long as the conductivities
are not grossly different and the regions are not separated by nonconducting materials.
The circulating eddy currents induced inside a prolate homogeneous spheroidal
model of the human body immersed in a uniform horizontal or vertical magnetic field
are shown in Figure 1.3. The induced electric fields are polarization dependent in that
they are always in a plane perpendicular to the magnetic field. The eddy current loop is
the largest when the dimension of the homogeneous region is the largest.
Eddy current
loop
Body model
H field
H field
FigurE 1.3 Circulating eddy currents induced inside a prolate homogeneous model of the
human body immersed in a uniform horizontal or vertical magnetic field.