Imagine two coaxial cylinders, one that is a volume with radius $Ra$ (and charge per unit lenght $-\lambda$) and another one that is just a surface with radius $Rc$ (and charge per unit lenght $+\lambda$), with $Rc > Ra$. What is the magnitude of the electric field everywhere in this distribution?
So the answer I have is this:
$$ E(r) =
\begin{cases}
0, & \text{, if $r < Ra$} \\
\frac{1}{2\pi \mathcal{E}_0}\frac{\lambda}{r}, & \text{, if $Ra<r<Rc$} \\
0, & \text{, if Rc < r}
\end{cases}
$$
My questions regard all the three positions. Why is the Electric field zero in the $r<Ra$ and the $Rc<r$ regions? And in the middle region, shouldn't the electric field be the sum of the fields created by the two charges?
Best Answer
This can be answered easily on the theorem of Gauss law.. In the three cases consider a imaginary cylinder at first radius
Notice that charge enclosed in first case is 0 second case is λ*l and third case is again 0
Thus E.2πr*l=charge enclosed/epsilon Putting values give desired result