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When solving E&M boundary problems, we usually use the condition that the electric potential should be continuous across the boundary. Why is that?
harshant said:i am wondering whether there is a mathematical proof to show that the potential is continuous everywhere except for point charges.
ahrkron said:When solving E&M boundary problems, we usually use the condition that the electric potential should be continuous across the boundary. Why is that?
letitbea said:so what's the final conclusion? if i got two dielectrics, the first one in x<0 and the other one in x>0, and a surface charge exists at x=0, will the potential be continuous at x=0 or not?
The electric potential is continuous because it is a scalar quantity that represents the potential energy per unit charge at a given point in space. This means that the electric potential at any point is dependent on the surrounding points, and there are no sudden changes or breaks in the potential.
The continuity of electric potential is directly related to the continuity of electric fields. This means that electric fields will also be continuous, with no sudden changes or breaks. In other words, a change in the electric potential will result in a change in the electric field, and vice versa.
In most cases, the continuity of electric potential is true. However, there are certain situations where this may not hold, such as at the edges of conductors or at points where there are large concentrations of charge. In these cases, the electric potential may not be continuous.
Continuity is important in understanding electric potential because it allows us to make predictions and analyze the behavior of electric fields and charges. Without continuity, it would be difficult to determine the effects of changes in electric potential and how they relate to changes in electric fields.
In general, the continuity of electric potential cannot be violated. This is because electric potential is a fundamental concept in electromagnetism and is based on the principles of conservation of energy and charge. However, as mentioned earlier, there are certain situations where the continuity may not hold, but these are exceptions rather than the norm.