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Re : Why can't elof be discontinuous :proof 
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#1
Jul914, 04:25 AM

P: 69

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." 


#2
Jul914, 06:45 AM

Sci Advisor
Thanks
PF Gold
P: 1,908

You can cast this into a more mathematical form by:
a. Noting that you are working with a vector field  there is a direction (and magnitude) at each point in space b. The field lines are tangent to the vectors (parallel) at each point; the construction is done by tracing the line that "flows" from point to point. This construction is what guarantees the continuity. c. The divergence theorem proves that there can be no field lines which do not terminate on sources/sinks, which are your charges. The fundamental assumption is that you have a vector field; this comes from the vector nature of forces, and that the "field of forces" exists everywhere. Your proof seems to be equivalent to this. 


#3
Jul914, 08:35 AM

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PF Gold
P: 11,923

Electric Fields are fields. The 'lines of force' representation of a field is not rigorous and it is not a good idea to try to take such a simple model and fit it to every phenomenon.



#4
Jul914, 08:55 AM

P: 69

Re : Why can't elof be discontinuous :proof
it was just a question in my paper for school exams preparation that came and i went thinking till this point So just small question Is there any blunder here(please a bit simpler way) 


#5
Jul914, 09:38 AM

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PF Gold
P: 11,923




#6
Jul914, 02:33 PM

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HW Helper
PF Gold
P: 1,991

1. E_normal is continuous across the surface. This follows from the divergence theorem applied to div E=0 (for a charge free region). This means E must be continuous along its vector direction. 2. E_tangential is continuous across the surface. This follows from Stokes' theorem applied to curl E=dB/dt. This means that E cannot have a discontinuous change in direction. 


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