Proving electric lines of forces can't be discontionous in charge free

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SUMMARY

The discussion centers on the impossibility of electric lines of force being discontinuous in charge-free regions, as established by Gauss' Law. The user proposes a proof using a Gaussian surface to illustrate that if electric field lines were discontinuous, the electric flux would not equal zero, contradicting the assumption of no enclosed charge. The consensus is that the continuity of electric field lines is inherent to their definition and not something that requires proof. The conversation highlights the foundational principles of electrostatics and the application of Gauss' Law in understanding electric fields.

PREREQUISITES
  • Understanding of Gauss' Law in electrostatics
  • Familiarity with electric field lines and their properties
  • Basic knowledge of Gaussian surfaces
  • Concept of electric flux and its calculation
NEXT STEPS
  • Study the implications of Gauss' Law in different charge distributions
  • Explore the concept of electric field lines in various electrostatic scenarios
  • Investigate the relationship between electric field lines and potential energy
  • Examine the behavior of test charges in electric fields
USEFUL FOR

Students of physics, educators teaching electrostatics, and researchers exploring electric field theories will benefit from this discussion.

namanjain
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Hey guys
i had a question in my paper
why electrostatic field lines cannot be discontinuous in charge free region

i guessed a weird (but an innovative proof)
Tell me is it correct

So here it goes
"Let's assume that ELOF can be discontinuous

Then i draw a diagram of broken electric field
Now at one of the two free ends i assumed a small Gaussian volume(Only the free end)
Now using gauss law
ø:FLUX
ø = ∑Qenclosed/ε
ELOF ARE ENTERING BUT NOT ESCAPING SO ø≠0
BUT ∑qENCLOSED=0
SO OUR ASSUMPTION IS FALSE
H.P."
 
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Gauss' law sort-of assumes that field lines cannot be discontinuous: so, by invoking it like that you are assuming the statement you are supposed to be proving.
Note: you don't need more than one free end in the hypothetical diagram.

The property is more part of the definition of "field line" so it is not something you prove exactly.
I suppose you could look at the consequences in terms of a small test charge... it travels along a field line to the end, then what?

You describe the Gauss' law argument as "novel" - have you been provided with a different "proof"?
 

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