I Determining continuity using Gauss' law

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Gauss' law effectively determines the discontinuity of the electric field at points on a surface charge, where the normal component of the electric field experiences a jump proportional to the surface charge. For non-singular volume-charge distributions, there are no discontinuities in the electric field, as confirmed by the Gauss pill-box argument. The discussion raises the possibility of using alternative methods to prove this concept without relying solely on Gauss' law. Clarifications regarding these concepts are anticipated in future posts. Understanding these principles is crucial for analyzing electric fields in various charge distributions.
Mike400
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I know how Gauss law helps us to calculate the discontinuity at a point on the surface of a surface charge.

Similarly using Gauss law, is there a way to determine the continuity at other points of electric field due to a surface charge or the continuity at all points of electric field due to a volume charge?
 
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I don't understand the question. If there's a surface charge, the normal component of the electric field jumps by that surface charge (modulo some factors depending on the system of units). If you have a non-singular volume-charge distribution there are no discontinuities.
 
vanhees71 said:
If you have a non-singular volume-charge distribution there are no discontinuities.
Can we prove it using Gauss law?
 
Sure, just use the "Gauss pill-box argument" to a situation where you have a non-singular charge distribution.
 
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Thanks a lot... Anyway I have to clear some confusions regarding that. I will post my confusions tomorrow... I am so sleepy
 
vanhees71 said:
If you have a non-singular volume-charge distribution there are no discontinuities.
Are there any other simple methods to prove it without using Gauss law?
 
Thread 'Gauss' law seems to imply instantaneous electric field'

Thread 'Gauss' law seems to imply instantaneous electric field'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
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Thread 'Do electron density waves accompany EM waves in coaxial cables?'

Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following transverse part $$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2} = \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$ and longitudinal part...
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