Concentric cylinders and grounding

[Allday]

OK, so we have a coaxial cable that consists of a solid cylinder at the core and two concentric cylindrical shells. All the components are conductors. The outer surface of the outer cylinder is grounded and the inner solid cylinder has a linear charge density of lambda.

Disregarding the gounding for now we know that this inner charge will induce charges on the outer shells. negative lambda on the inner surface of the inner shell, positive lambda on the outer surface of the inner shell, negative lambda on the inner surface of the outer shell, and positive lambda on the outer surface of the outer shell.

The question is will the grounding of the outer surface of the outer shell allow electrons to flow there and cancel the positive lambda on the outer surface of the outer shell? Grounding means the potential is zero, but in this case does it also mean the charge is zero? Any suggestions on how to discuss this process in a lecture would be helpfull.

Thanks

 

[ehild]

The question is will the grounding of the outer surface of the outer shell allow electrons to flow there and cancel the positive lambda on the outer surface of the outer shell? Grounding means the potential is zero, but in this case does it also mean the charge is zero? Any suggestions on how to discuss this process in a lecture would be helpfull.

Thanks

The surface charge density at the outer surface of the outer shell becomes zero. So this shell gets a net charge equal in magnitude and of opposite sign to that of the inner core.


ehild

 

[wais]

for sharing this interesting concept about concentric cylinders and grounding. It is important to understand the role of grounding in this system.

First, let’s clarify what grounding means in this context. Grounding refers to connecting the outer surface of the outer cylinder to a large conducting object or the Earth itself. This allows excess charge to flow out of the system and neutralize it. In other words, grounding helps to maintain a constant potential throughout the system.

Now, let’s consider the effect of grounding on the charges induced on the outer shells. As you mentioned, the presence of the inner charge will induce charges on the outer shells. However, the grounding of the outer surface of the outer shell will also induce a flow of electrons towards it, cancelling out the positive lambda on its outer surface.

In this case, grounding does not necessarily mean that the charge on the outer surface of the outer shell will be zero. It just means that the potential will be zero, as any excess charge will be neutralized by the grounding. This is an important distinction to make in understanding the behavior of this system.

In terms of discussing this process in a lecture, it would be helpful to first explain the concept of grounding and its purpose in maintaining a constant potential. Then, you can discuss how grounding affects the charges induced on the outer shells in the context of this system. It may also be helpful to provide a diagram or demonstration to visually illustrate the effects of grounding on the system.