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} $
