Why can't a uniform electric field be described by E=\frac{kq}{r^2}?

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temaire
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This is not a homework question, but I was just wondering, why can't a uniform electric field be described by the formula [tex]E=\frac{kq}{r^2}[/tex] ?
 
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When we have to case of a uniform electric field, it means that the field is constant in a region of space. In the definition of the above electric field, what happens to the electric field as r increases and decreases.