Question

The electric field in a region is radially outward with magnitude $E=A{\gamma }_0$. The charge contained in a sphere of radius ${\gamma }_0$ centered at the origin is

• A. $\frac{1}{4\pi {ϵ}_0}A{\gamma }_0^3$
• B. $4\pi {ϵ}_{0}A{\gamma }_0^3$
• C. $\frac{4\pi {ϵ}_{0}A}{{\gamma }_0}$
• D. $\frac{1}{4\pi {ϵ}_0}\frac{A}{{\gamma }_0^3}$

Answer 1

The correct option is B $4\pi {ϵ}_{0}A{\gamma }_0^3$

Flux linked with the given sphere $\varphi =\frac{Q}{{ϵ}_0}$;
where Q = Charge enclosed by the sphere.
Hence $Q=\varphi {ϵ}_0=\left(EA\right){ϵ}_0$
$\Rightarrow Q=4\pi \left({\gamma }_0^2\right)\times A{\gamma }_0{ϵ}_0=4\pi {ϵ}_{0}A{\gamma }_0^3$.