Continuity equation of the electric field

In summary, according to the continuity equation of the electric field, a decrease in cross-section area will result in an increase in electric field strength. This has been observed in previous studies on electroporation, where reducing the cross-section area of microchannels used for cell trapping leads to an amplification of the electric field strength. The equations that explain this phenomenon involve the electrokinetic and dielectrophoretic velocities, as well as the electric field contour and lines around the constriction region.
  • #1
speaknow
3
0
According to the continuity equation of the electric field (i.e., ▽·Ε = 0) a decrease in cross-section area will increase the electric field strength, Why is that?
 
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  • #2
You're going to have to be more specific. Ddecrease the cross-section area of what exactly?
 
  • #3
Thanks for your reply, in previous studies on electroporation reducing the cross-section area of microchannels (microfluidics)used for cell trapping will have an amplification on the electric field strength. I want to understand the equations behind this phenomena.
 

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  • #4
You're going to make us slowly squeeze this out of you bit by bit, aren't you.

OK, for some reason that you won't tell us, possible related to the U's in the picture that you won't define, all the electric field lines from one region go into the other. Since for some other reason you won't tell us, they are excluded from the central region except for the joining channel, since the number is constamt and the area is smaller, the density has to go up.
 
  • #5
UEK and UDEP are the electrokinetic and dielectrophoretic velocities, respectively. UDEP,s and UDEP,n👀 represent the dielectrophoretic velocity components tangential and normal to a streamline, respectively. The background shows the electric field contour (the darker the higher) and the electric field lines around the constriction region in the absence of cells. 👀
 

1. What is the continuity equation of the electric field?

The continuity equation of the electric field is a mathematical expression that describes the relationship between the flow of electric charge and the electric field. It states that the change in electric charge within a given volume is equal to the net flow of electric current into or out of that volume.

2. Why is the continuity equation of the electric field important?

The continuity equation of the electric field is important because it is a fundamental principle of electromagnetism that helps us understand how electric charge and electric current behave in different situations. It is also used in many practical applications, such as circuit analysis and the design of electronic devices.

3. How is the continuity equation of the electric field derived?

The continuity equation of the electric field is derived from the laws of conservation of charge and energy. It can also be derived from Maxwell's equations, which are a set of fundamental equations that describe the behavior of electric and magnetic fields.

4. What are some real-world examples of the continuity equation of the electric field?

Some real-world examples of the continuity equation of the electric field include the flow of current in a circuit, the behavior of electric currents in a plasma, and the movement of electrons in a semiconductor device.

5. How does the continuity equation of the electric field relate to Kirchhoff's current law?

Kirchhoff's current law, also known as Kirchhoff's first law, states that the sum of currents entering a node in an electrical circuit is equal to the sum of currents leaving that node. This is essentially a restatement of the continuity equation of the electric field, which states that the net flow of electric current into or out of a given volume must be equal to the change in electric charge within that volume.

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