Question

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

• A. $\frac{1}{4 \pi \varepsilon_0} Ar ^3$
• B. $4 \pi \varepsilon_0 Ar ^3$
• C. $\frac{1}{4 \pi \varepsilon_0} \frac{ A }{ r ^3}$
• D. $\frac{4 \pi \varepsilon_0 A }{ r ^3}$

Answer 1

Answer: (B)

$E=\frac{q}{4 \pi \varepsilon_0 r^2}$
$ \Rightarrow A r=\frac{q}{4 \pi \epsilon_0 r^2}$
$ \Rightarrow q=4 \pi \varepsilon_0 A r^3$