Number of fields line originating from 1 C charge

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I'm not sure of the answer to your specific question. Using Gauss's Law, if you consider Q and ε, their quotient has units of Coulomb-metres per Farad, or equivalently volt-meters. This doesn't sound like what I'd be expecting for a "count" or number of anything, really. And I suppose its proponents would get around the problem of fractions of lines by dividing "lines" into "microlines" or something?

In the video, by saying the number of lines you may choose to draw is initially arbitrary, he means that on diagrams you'll usually draw only a representative number of lines, sufficient to illustrate the situation.
 
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