Why does Coulomb's Law include a pi in the denominator?

In summary, the conversation revolves around calculating the electric field a distance r from a uniform straight infinite line charge using both Gauss' Law and Coulomb's law. The answers obtained from both methods are the same, except for a pi that remains in the denominator of Coulomb's law. The user is seeking help to understand this discrepancy and correct any errors in their calculation. Through further discussion and writing out the steps, the user discovers and corrects a simple integration error.
  • #1
Old Guy
103
1

Homework Statement


I'm sure I'm missing something simple here, but to the point:

I calculate the electric field a distance r from a uniform straight infinite line charge using Gauss' Law and get an answer; I do the same calculation using Coulomb's law and get the same answer but a pi remains in the denominator (that was not there in the Gauss' Law solution). I don't know how to enter the equation here, but in both answers the numerator is the linear charge density. The Gauss' Law denonminator is 2r times epsilon; Coulomb's law denominator is 2(pi)r times epsilon. Help!


Homework Equations


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The Attempt at a Solution


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  • #2
Can you write out each of your steps? Maybe then one of us'll be able to spot the error.
 
  • #3
Well, thanks for the fast response. In writing out the steps as you requested I caught a (dumb) integration error - I'm straight now. Thanks.
 
  • #4
Old Guy said:
Well, thanks for the fast response. In writing out the steps as you requested I caught a (dumb) integration error - I'm straight now. Thanks.

You can't imagine how many times I've been stumped on a problem only to realize my error while explaining what I did to someone. :)
 

Related to Why does Coulomb's Law include a pi in the denominator?

What is the Coulomb Constant?

The Coulomb Constant, also known as the electric constant or the permittivity of free space, is a physical constant that describes the relationship between electric charge and electric force in a vacuum.

How is the Coulomb Constant calculated?

The Coulomb Constant is calculated by taking the product of the speed of light, the vacuum permeability, and the square of the elementary charge. This gives a value of approximately 8.9875 × 10^9 N·m^2/C^2.

What units is the Coulomb Constant measured in?

The Coulomb Constant is typically measured in units of Newtons times meters squared per Coulomb squared (N·m^2/C^2). It can also be expressed in terms of other units, such as Farads per meter (F/m).

What role does the Coulomb Constant play in Coulomb's Law?

The Coulomb Constant is a crucial factor in Coulomb's Law, which states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Without the Coulomb Constant, this relationship would not be possible.

Why is the Coulomb Constant important in the field of electromagnetism?

The Coulomb Constant is important in electromagnetism because it allows us to understand and quantify the relationship between electric charge and electric force. It is used in various calculations and equations to predict and manipulate electric fields and forces. Without the Coulomb Constant, our understanding and application of electromagnetism would be limited.

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