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This question already has an answer here:

I would like to draw an electric field. But from the condition of the electric field itself, the lines(or flux) should not be created again in the process of getting farther from the origin(or charge).

But as you can see from the output of StreamPlot below, it creates several, more stream lines in the middle of stream lines directly from the origin getting spread.

k = 1; x0 = 0; y0 = 0;
StreamPlot[{k (x - x0)/((x - x0)^2 + (y - y0)^2)^(3/2), 
  k (y - y0)/((x - x0)^2 + (y - y0)^2)^(3/2)}, {x, -50, 50}, {y, -50, 
  50}]

enter image description here

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marked as duplicate by Mr.Wizard plotting Jun 18 '16 at 7:50

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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Have a look at http://demonstrations.wolfram.com/ElectricFieldLinesDueToACollectionOfPointCharges/, which is an excellent demonstration for teaching electrostatics.

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