Question

Imagine the electric field in a certain region of space is
radial with E_{r} = ar^{2}, where a is a constant.
Is this empty space? Use Gauss' Law to prove your answer. PLEASE
SHOW ALL WORK!!!!

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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