Discrepancies with Coulombs law?

[carnivalcougar]

Homework Statement

E obeys Coulombs law, i.e. E is proportional to 1/r^2. However, between a parallel plate, E = constant and in coaxial cylinders E is proportional to 1/r. What is the explanation for these discrepancies?

Homework Equations

The Attempt at a Solution

I think that Coulomb's law is only for point charges. Coulomb's Law does not state that E is proportional to 1/r². It states that E due to a stationary point charge is proportional to 1/r². Parallel electrodes and concentric electrodes aren't stationary point charges, so there's no reason to expect the field they produce to be proportional to 1/r².

 

[Simon Bridge]

... so what you are saying is that Coulombs law is just not a general physical law? It only applies for a single case? In which case - why bother teaching it? Should it not be taught as a special case of a more general rule instead?

And if Coulombs law is not general, then why would anyone think that the examples represent contradictions at all? Surely it should come as no surprise that different situations follow different rules?

Consider: The parallel plates and coax situations are made out of point charges - each point charge obeys coulombs law you say - but the configurations do not? How so?

 

[Chestermiller]

Homework Statement

E obeys Coulombs law, i.e. E is proportional to 1/r^2. However, between a parallel plate, E = constant and in coaxial cylinders E is proportional to 1/r. What is the explanation for these discrepancies?

I think that Coulomb's law is only for point charges. Coulomb's Law does not state that E is proportional to 1/r². It states that E due to a stationary point charge is proportional to 1/r². Parallel electrodes and concentric electrodes aren't stationary point charges, so there's no reason to expect the field they produce to be proportional to 1/r².

Is it your understanding that Coulomb's law is a scalar equation or a vector equation? Is it your understanding the Coulomb's law can only be applied to a single point charge, or can it be applied to multiple charges by superimposing their individual contributions to the electric field?

 

[carnivalcougar]

Consider: The parallel plates and coax situations are made out of point charges - each point charge obeys coulombs law you say - but the configurations do not? How so?

can it be applied to multiple charges by superimposing their individual contributions to the electric field?

I know you can take the integral of the region containing the charge where each infinitesimal unit of space is a point charge. However, this class is not calc-based. If every unit of space were a point charge then I suppose the electric field would be constant between parallel plates.

I'm still not sure why the electric field would be proportional to 1/r in the coaxial cylinder situation.

 

[Chestermiller]

I know you can take the integral of the region containing the charge where each infinitesimal unit of space is a point charge. However, this class is not calc-based. If every unit of space were a point charge then I suppose the electric field would be constant between parallel plates.

I'm still not sure why the electric field would be proportional to 1/r in the coaxial cylinder situation.

If the number of charges on the two cylinders are equal, then the number of charges per unit area on the inner cylinder is higher than the number of charges per unit area on the outer cylinder. So the electric field is stronger toward the inner cylinder.

 

[Simon Bridge]

I know you can take the integral of the region containing the charge where each infinitesimal unit of space is a point charge. However, this class is not calc-based.

Then you need to give a word-answer instead of a calculus one.
What is the physics that the calculus is describing?
(Note: calculus is a fancy way of adding stuff up.)

The basic question may be rewritten:
If coulombs law is general - then how does it give rise to fields that are not 1/r²?

The path to a solution has been hinted at by Chestermillar in post #3.
What the question is after is some statement that shows that you understand the course material about how electric fields work. Therefore you need to be able to state your understanding.

 

[carnivalcougar]

Coulomb's law can be applied to multiple charges. If there were only two point charges, the inverse square law would apply because there would be no other forces from other charges acting on them. However, if each infinitesimal unit of space is a point charge, they can be integrated which adds them up. The forces exerted on each point charge will be the sum of the forces of all of the other point charges leading to a uniform electric field between two plates.

With coaxial cylinders, the area of the inner cylinder is smaller than the area of the larger cylinder. This leads to a larger amount of point charges per unit area on the smaller cylinder creating a stronger electric field on this cylinder creating an inversely proportional relationship between the electric field and the distance from the cylinder.

Is this an accurate understanding of what is going on?

 

[Simon Bridge]

You should be able to avoid using the word "integrated" or any mention of calculus (unless your course notes mention calculus the same way). I would expect to see some mention of the fact that coulomb's law is a vector equation and how that affects the sum. In general. But you are getting the idea.