Discrepancies with Coulombs law?

In summary, Coulomb's law can be applied to multiple charges by summing up their individual contributions to the electric field. This can result in variations from the inverse square relationship, such as a constant electric field between parallel plates and an inversely proportional relationship between the electric field and distance from coaxial cylinders. The key factor is the distribution of charges and the resulting effect on the electric field.
  • #1
carnivalcougar
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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.
 
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  • #2
... 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?
 
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  • #3
carnivalcougar said:

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?
 
  • #4
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.
 
  • #5
carnivalcougar said:
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.
 
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  • #6
carnivalcougar said:
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.
 
  • #7
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?
 
  • #8
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.
 

FAQ: Discrepancies with Coulombs law?

What is Coulomb's law and how does it relate to discrepancies?

Coulomb's law is a fundamental law of electrostatics that describes the force between two charged particles. It states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Discrepancies with Coulomb's law refer to situations where the predicted force between two charged particles does not match the actual force observed.

What are the causes of discrepancies with Coulomb's law?

There are several possible causes of discrepancies with Coulomb's law. One common cause is the presence of other forces, such as gravitational or magnetic forces, that can also affect the particles. Another cause could be measurement errors or inaccuracies in the values of the charges or distances used in the calculation.

How can discrepancies with Coulomb's law be minimized or eliminated?

To minimize or eliminate discrepancies with Coulomb's law, it is important to carefully control and measure all factors that could affect the force between the particles. This includes controlling for other forces and ensuring accurate measurements of charge and distance. Additionally, conducting multiple trials and averaging the results can help to reduce the impact of any measurement errors.

Are there any real-world applications where discrepancies with Coulomb's law are important?

Yes, discrepancies with Coulomb's law can be important in many real-world applications, such as in the design and operation of electrical devices and systems. In these cases, accurately predicting the forces between charged particles is crucial for ensuring the proper functioning and safety of the devices.

What further research is being done to better understand and address discrepancies with Coulomb's law?

There is ongoing research in the field of electrostatics to better understand the underlying principles of Coulomb's law and to identify any potential modifications or extensions to the law that could better explain observed discrepancies. Additionally, advancements in technology and measurement techniques are constantly being developed to improve the accuracy of calculations and reduce discrepancies with Coulomb's law.

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