Find the electric field at an arbitrary position

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Homework Help Overview

The problem involves using Gauss’s Law to determine the electric field at an arbitrary position within the hollow region between two concentric conducting cylinders. The inner cylinder has a radius 'a' and a charge per unit length 'λ', while the outer cylinder has an inner radius 'b' and the same charge per unit length.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the symmetry of the problem, identifying it as cylindrical. Questions are raised about the application of Gauss's Law and how to set up the integral for the electric field between the cylinders.

Discussion Status

Some participants have provided guidance on constructing a hypothetical Gaussian surface and evaluating the integral. There is an acknowledgment of confusion regarding the setup of the integrand, indicating that the discussion is still active and exploratory.

Contextual Notes

Participants note that the region between the cylinders has a charge density of ρ=0, and there is a resemblance to a coaxial cable configuration. The discussion reflects uncertainty about the integration process and the contributions to the electric field from the cylinders.

BPBAIR
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Problem:

Use Gauss’s Law to find the electric field at an arbitrary position r in the hollow region (ρ =0) between two concentric conducting cylinders. The inner cylinder has radius a and bears a constant charge per unit length, λ, while the outer cylinder has inner radius b and bears the same charge per unit length.

Equation:
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Solution:
Not really sure, where to go with this from a geometric point of view.
 
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Ok, first of all, what symmetry can you use in this problem? Is it spherical, cylindrical, etc?

Also, just think of the definition of Gauss' Law, and see where you can apply it here.
 
Well it would have cylindrical symettry. And the field would be completely radial b/c the top and bottom components would cancel leaving only the integral for the sides. rho=0 for in between the two cylinders, which resembles a coaxial cable with a space between the two cylinders. If anyone could help me furtehr on this problem, I would appreciate it. I am confused on how to setup the integrand since it is between two cylinders.
 
BPBAIR said:
Well it would have cylindrical symettry. And the field would be completely radial b/c the top and bottom components would cancel leaving only the integral for the sides. rho=0 for in between the two cylinders, which resembles a coaxial cable with a space between the two cylinders. If anyone could help me furtehr on this problem, I would appreciate it. I am confused on how to setup the integrand since it is between two cylinders.

Ok. First of all, you need to construct a hypothetical gaussian surface over which you need to evaluate the surface integral, which in this case will be a cylinder because of the symmetry. First, can you find out what is the elemental area you're integrating over? Can you proceed from here to find the field?
 
figured it out. only the inner cylinder will contribute to the field. from there it is two simple intergrals and the gaussian turns out yo be [ lambda / (2*pi*epsilon*r) ] = E
 

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