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

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Question:

Two thin, long and  hollow cylinders with length ll 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 ϵ0ϵ0 in any expressions.

There are two charged coaxial cylinders of length l. The inner cylinder has radius r with charge +Q and the outer cylinder has radius r + d with charge -Q.

Part 1)

Using Gauss' Law or any other method derive an expression for the magnitude of the electric field EE at a point  RR from the axis of the two cylinders, where r<R<r+dr<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+dVr=ΔV=Vr+dVr= 

 

Part 3)

Find the magnitude of the electric field EE at a point  RR from the axis of the two cylinders, where R>r+dR>r+d

E=E= 

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