B-field Exposure From Induction Cooking Appliances 70
7 Approximation of Induced Current Density
As shown in Chapters 6.1.2, 6.1.3, 6.1.4 and in Table 14, the B-fields measured around the
induction cookers are largely non-uniform.
The ICNIRP guidelines [2] state that the reference levels are intended to be spatially averaged
values over the entire body of the exposed individual, but with the important provision that
the basic restrictions on localized exposure are not exceeded. However, reliable estimations of
the current density J induced in the body at close proximity to the induction cookers can only
be obtained by appropriate simulation tools. Since these evaluations were not within the scope
of this project, we approximate J based on very simple models in order to identify possible
concerns of strong violations of the basic restrictions.
Figure 54: Magnetic field model used to roughly calculate the induced current density J in the
body at close proximity to the induction cookers. The B-field does not depend on the position.
The magnetic field model shown in Figure 54 was used to roughly evaluate the induced current
density J. The model assumes that the body has a homogeneous and isotropic conductivity,
using a plane wave approximation of the B-field. The induced current density J is derived from
Faraday’s law of induction (simple circular conductive loop model, Equation (10)) and Ohm’s
law (Equation (11)):
I
L
E dl = −
Z
S
∂B
∂t
· dA (10)
J = σE (11)
where E and B are the electric and magnetic fields, L and S are the contour and the surface,
and J and σ are the current density and the conductivity, respectively.
In this model, B does not depend on the position (see Figure 54). The B-field is given by
B(x, y, z, t) = B(z, t) = B
0
sin(ωt), with ω = 2πf the angular velocity. The electric field E is
derived from Faraday’s law for a pure sinusoidal field at frequency f:
I
L
E dl = 8aE(t) (12)
−
Z
S
∂B
∂t
· dA = 4a
2
B
0
ω cos (ωt) (13)
