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

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