Question: question two thin long and hollow cylinders with length ll...

Question:

Two thin, long and  hollow cylinders with length l$l$ are charged with equal but opposite charges +Q$+Q$ and −Q.$-Q.$ The inner cylinder has a radius r,$r,$ while the outer cylinder has a radius r+d,$r+d,$ as shown in the figure. In this question use permittivity of free space ϵ0${ϵ}_0$ in any expressions.

Part 1)

Using Gauss' Law or any other method derive an expression for the magnitude of the electric field E$E$ at a point  R$R$ from the axis of the two cylinders, where r<R<r+d$r<R<r+d$. 

E=$E=$ 

 

Part 2)

Using your result in Part 1)  derive  an expression for the potential difference between the two cylinders.

ΔV=Vr+d−Vr=$\mathrm{\Delta }V=V_{r+d}-V_r=$ 

 

Part 3)

Find the magnitude of the electric field E$E$ at a point  R$R$ from the axis of the two cylinders, where R>r+d$R>r+d$. 

E=$E=$