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My E&M textbook says the following: The electric field at position $r= (x,y,z)$ generated by a point charge $q$ at the origin is given by $$\vec{E}(r) =\frac{q}{4π\epsilon_0r^2}\hat r=\frac{q}{4π\epsilon_0}\frac{x\hat i+y\hat j+z\hat k}{(x^2+y^2+z^2)^{\frac{3}{2}}}$$ I understand Coulomb's Law, but how is the right side of the equation derived?

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The electric field generated by a point charge is radial, which means the $\hat{i}$ on the left should actually be: \begin{equation} \hat{r}=\frac{\vec{r}}{r}=\frac{x\hat{i}+y\hat{j}+z\hat{k}}{\sqrt{x^2+y^2+z^2}} \end{equation}

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