Determining continuity using Gauss' law

In summary, the conversation discusses the use of Gauss law to calculate the discontinuity at a point on the surface of a surface charge. The person asks if there is 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. It is mentioned that a non-singular volume-charge distribution does not have discontinuities, and this can be proven using the "Gauss pill-box argument". The person also asks if there are other methods to prove this without using Gauss law.
  • #1
Mike400
59
6
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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  • #2
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.
 
  • #3
vanhees71 said:
If you have a non-singular volume-charge distribution there are no discontinuities.
Can we prove it using Gauss law?
 
  • #4
Sure, just use the "Gauss pill-box argument" to a situation where you have a non-singular charge distribution.
 
  • Like
Likes Mike400
  • #5
Thanks a lot... Anyway I have to clear some confusions regarding that. I will post my confusions tomorrow... I am so sleepy
 
  • #6
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?
 

What is Gauss' law?

Gauss' law is a fundamental law in physics that relates the electric flux through a closed surface to the net charge enclosed by that surface. It is one of the four Maxwell's equations that describe the behavior of electric and magnetic fields.

How is Gauss' law used to determine continuity?

Gauss' law can be used to determine the continuity of a charge distribution by calculating the electric flux through a closed surface surrounding the distribution. If the electric flux is non-zero, it indicates the presence of a net charge and therefore continuity is not satisfied. If the electric flux is zero, it indicates that there is no net charge and continuity is satisfied.

What is continuity?

Continuity is a fundamental principle in physics that states that the amount of charge entering a closed surface must be equal to the amount of charge leaving the surface. This principle ensures that charge is conserved in a given system.

What is the importance of determining continuity using Gauss' law?

Determining continuity using Gauss' law is important because it allows us to check if a given charge distribution is physically possible. If continuity is not satisfied, it means that there is a violation of charge conservation and the distribution is not physically realistic.

What are the limitations of using Gauss' law to determine continuity?

Gauss' law can only be used to determine continuity for static charge distributions. It cannot be applied to time-varying or dynamic systems. Additionally, it assumes that the electric field is uniform over the closed surface, which may not always be the case in real-world situations.

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