I have difficulty in visualizing the divergence of vector fields.

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Hi all. I have difficulty in visualizing the concept of divergence of a vector field. While I have some clue in undertanding, in fluid mechanics, that the divergence of velocity represent the net flux of a point, but I find no clue why the divergence of an electric field measures the charge denity?

Can anyone tell me how to interpret the divergence of a vector field? Please kindly help.
 

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I'll try...

Gauss' Law says that the flux of an E field is proportional to the total charge within the surface that you compute the flux.

Using integral theorems, the flux is a volume integral of the divergence. But, the total charge is the volume integral of charge density. This works out for arbitrary volumes so the divergence must be proportional to the charge density.
 

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