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in the case of uniform electric field why should electric field lines be equally spaced? Is this related to advanced math stuff?

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Electric field lines are drawn typically for two reasons: to either show the direction of force a positively charged particle would feel if placed at that point, or to show the strength of the electric field at a given point in comparison to another point. If the line density is greater in one region than in another, the author/artist is typically trying to convey that the electric field is strong there. A uniform electric field is, by definition, the same strength and direction everywhere. Meaning, the line density and direction of each electric field line should be the same.

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There are an infinite number of “field lines”. One passes through every point. People draw a few of them, uniformly spaced, for a uniform field to indicate that the field is uniform. Otherwise, the field would look non-uniform.

“Field lines” are just a visual aid. Physically, there are no “lines in the field”. The field is really a vector, with a magnitude and a direction, at every point. The “lines” show you the direction of the vectors. The spacing of the lines gives you some sense of the magnitude of the vectors. Closer lines mean larger magnitude.

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  • $\begingroup$ In a nice three dimensional sketch, the density of field lines should be proportional to the field strength. $\endgroup$
    – R.W. Bird
    Commented Feb 20, 2020 at 18:23

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