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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?
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.
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.
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.
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.
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.