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Imagine the electric field in a certain region of space is radial with Er = ar2,...

Imagine the electric field in a certain region of space is radial with Er = ar2, where a is a constant. Is this empty space? Use Gauss' Law to prove your answer. PLEASE SHOW ALL WORK!!!!

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Answer #1

In this question, the electric field is given by,

, where a is a constant,

Now,

From the differential form of Gauss's law, we can write,

, where is the charge density and is the permittivity of free space.

For the present case, charge density .

So the space under consideration is not charge free. So, we can not call it empty space.

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