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Induction
Currents from Circular Coils
Introduction
A time-varying current induces a varying magnetic field. This field
induces currents in neighboring conductors. The induced currents are
called eddy currents. The following model illustrates this phenomenon
巴沙鱼的家常做法by a time-harmonic field simulation as well as a transient analysis,永远做自己
which provides a study of the eddy currents resulting from switching on
the source.
Two current-carrying coils are placed above a copper plate. They are
爱国爱党诗词surrounded by air, and there is a small air gap between the coils
and the metal plate. A potential difference provides the external
source. To obtain the total current density in the coils you must
take the induced currents into account. The time-harmonic ca shows
the skin effect, that is, that the current density is high clo to
the surface and decreas rapidly inside the conductor.
Model Definition
E Q U A T I O N
To solve the problem, u a quasi-static equation for the magnetic potential A : σ-∂--A ---- + ∇ × (μ–1μ–1∇ × A ) = σV coi -l
∂t 0 r2πr
coil
上海科技馆攻略Here μ0 is the permeability of vacuum, μr the relative permeability, σ the electric conductivity, and V coil the voltage over one turn in the coil. In the time-harmonic ca the equation reduces to
–1 –1 V
= ----------- j ωσA + ∇ × (μ0 μr ∇ × A ) σ 2πr
F O R C E S
The total electromagnetic force acting on region of space Ω can be obtained by integrating Maxwell ’s stress tensor on the delimiting boundary ∂Ω:
F =
nba得分排行T n dS
∂Ω The Force Calculation feature automatically performs the integral along the boundaries of the desired region, considering also the axisymmetric geometry of the problem. The computed force will be available in results processing as a global variable.
Results
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and
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Discussion
In the time-harmonic regime, the varying magnetic field induces
electrical currents in the metallic plate. The currents, in turn, act as sources of an opposing magnetic field “shielding ” the plate from the magnetic field. As a result of this phenomenon, the region in
which electrical currents are generated is confined in proximity of the surface and reduces in size wi
校园演讲稿th increasing frequency. Figure 1 and Figure 2 show the induced current density at 10 Hz and 300 Hz, respectively.
In this model, a time-domain study is performed to investigate the step respon of the system. Figure 3 displays a snapshot of the induced current density and magnetic flux density for the transient solution in a combined surface and arrow plot.
Finally, Figure 4 shows the total axial force between the coils and the plate as a function of time computed by the Force Calculation feature. For the chon current direction, the force is repulsive
(negative).
Figure 1: The ϕcomponent of the induced current density for the time-harmonic solution plotted together with a contour plot of the magnetic vector potential at a frequency of
10 Hz.
Figure 2: Plot of the same quantities at a frequency of 300 Hz.
