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From the Gauss law we know, $\nabla \cdot \vec{E} = \rho / \epsilon_0 $.

We have given that, $\vec{E}= kr^3 \hat {r}$

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Now I have problem to get the identified part. Can you please elaborate that?

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  • $\begingroup$ $E_{r} = kr^{3}$. $\endgroup$ – Felix Marin Jun 18 '14 at 19:18
  • $\begingroup$ I wanted to understand the the previous step? $\endgroup$ – Complex Guy Jun 18 '14 at 19:21
  • $\begingroup$ That's the formula for divergence spherical coordinates (when the force is radial). Gauss's Law applies to the usual electromagnetic fields (given by inverse square laws), not to an arbitrary $\vec E$. $\endgroup$ – Ted Shifrin Jun 18 '14 at 19:26
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See, e.g., Wikipedia for the formula for the various differential operators in cylindrical and spherical coordinates.

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