Electrostatics Question 699

Question: If electric field in a region is radially outward with magnitude $ E=Ar $ , the charge contained in a sphere of radius r centered at the origin is

Options:

A) $ \frac{1}{4\pi {\varepsilon _{0}}}Ar^{3} $

B) $ Ar^{3}4\pi {\varepsilon _{0}} $

C) $ \frac{1}{4\pi {\varepsilon _{0}}}\frac{A}{r^{3}} $

D) $ \frac{4\pi {\varepsilon _{0}}A}{r^{3}} $

Show Answer

Answer:

Correct Answer: B

Solution:

[b] $ E=\frac{q}{4\pi {\varepsilon _{0}}r^{2}}\Rightarrow Ar=\frac{q}{4\pi {\in _{0}}r^{2}} $

$ \Rightarrow q=4\pi {\varepsilon _{0}}Ar^{3} $



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