电磁场与电磁波第12讲焦耳定律边界条件电阻计算及第5章复习.ppt

Field and Wave Electromagnetic
电磁场与电磁波
2015.
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1. Current Density and Ohm’s Law
Review
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3. Equation of Continuity and Kirchhoff’s Current Law
2. Electromotive Force and Kirchhoff’s Voltage Law
Outside
the source
Inside
the source
E
Conducting medium










P
N





E





Impressed source
Ei
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We are now in a position to prove this statement and to calculate the time it takes to reach an equilibrium.
where 0 is the initial charge density at t = 0.
The time constant t is called the relaxation time(驰豫时间）.
铜，=×10-19S
An initial charge density 0 will decay to 1/e or % of its value in a time equal to
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For a homogeneous conducting medium
We know that a curl-free vector field can be expressed as the gradient of a scalar potential field. Let us write
Substitution of this equation into
yields a Laplace’s equation in  ; that is
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Two fields are found to be very similar in source-free region.
Steady Electric Current Field
Electrostatic Field
The electric current density J corresponds to the electric field intensity E, and the electric current lines to the electric field lines.
In some cases, since the steady electric current field is easy to be constructed and measured, the electrostatic field can be investigated based on the steady electric current field with the same boundary conditions, and this method is called electrostatic simulation.
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Capacitance


J
E
Resistance
Based on the equations for two fields, we can find the resistance and conductance between two electrodes as
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In certain situations, electrostatic and steady-current problems are not exactly analogous, even when the geometrical configurations are the same. This is because current flow can be confined strictly within a conductor (which has a very large  in comparison to that of the surrounding