Deriving Electric Field in a Charged Rod and Shell System"

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Homework Help Overview

The discussion revolves around deriving the electric field in a system consisting of a long straight conducting rod with a positive linear charge density and a cylindrical shell with a negative linear charge density. Participants are tasked with using Gaussian surfaces to analyze the electric field both inside the shell and outside the entire system.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to apply Gauss's law to derive the electric field in two regions: between the rod and the shell, and outside the shell. Some participants question the validity of the calculations presented and whether they address all parts of the problem. Others raise the point about the total enclosed charge being zero and its implications for the electric field.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the implications of the enclosed charge on the electric field, but there is no explicit consensus on the answers to the parts of the problem.

Contextual Notes

Participants are navigating the complexities of applying Gauss's law in the context of a system with both positive and negative charge densities. There are indications of confusion regarding the calculations and the assumptions made about the enclosed charge.

chillaxin
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A long straight conducting rod (or wire) carries a linear charge density of +2.0uC/m. This rod is totally enclosed within a thin cylindrical shell of radius R, which carries a linear charge density of -2.0uC/m.
A) Construct a Gaussian cylindrical surface between the rod and the shell to derive then electric field in the inner space as a function of the distance from the center of the rod.
B) Construct a Gaussian cylindrical surface outside both the rod and the shell to calculate the electric field outside the shell.

This is what i have so far.

E=q/4piEor^2
E=+2.0uC/m / 4pi8.85x10^-12(-2uC/m)^2
E=4.5x10^9Nm^2/C
 
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chillaxin said:
A long straight conducting rod (or wire) carries a linear charge density of +2.0uC/m. This rod is totally enclosed within a thin cylindrical shell of radius R, which carries a linear charge density of -2.0uC/m.
A) Construct a Gaussian cylindrical surface between the rod and the shell to derive then electric field in the inner space as a function of the distance from the center of the rod.
B) Construct a Gaussian cylindrical surface outside both the rod and the shell to calculate the electric field outside the shell.

This is what i have so far.

E=q/4piEor^2
E=+2.0uC/m / 4pi8.85x10^-12(-2uC/m)^2
E=4.5x10^9Nm^2/C
The field is certainly not constant in the region between the rod and the cylinder. Are these anwers to multiple parts? Just the first part?
 
Last edited:
Unless I'm mistaken, the total charge inclosed in the whole system is zero. If the enclosed charge is zero, the electric field is zero. Thus from what I can draw, the answer to B is zero. The answer to A requires using the enclosed charge to be the positive portion and then solving for E.
 

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