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

  • Thread starter Thread starter Old Guy
  • Start date Start date
  • Tags Tags
    Constant Coulomb
AI Thread Summary
The discussion revolves around a student's confusion regarding the presence of pi in the denominator when calculating the electric field from a uniform infinite line charge using Coulomb's Law, compared to the result from Gauss' Law. The student initially believes there is a discrepancy between the two methods, as Gauss' Law yields a simpler denominator. Upon further examination and detailing their steps, the student identifies a mistake in their integration process, resolving the issue. This highlights the importance of carefully reviewing calculations and the common experience of discovering errors through explanation. The conversation emphasizes problem-solving techniques in physics, particularly in electrostatics.
Old Guy
Messages
101
Reaction score
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


See above


The Attempt at a Solution


See above
 
Physics news on Phys.org
Can you write out each of your steps? Maybe then one of us'll be able to spot the error.
 
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.
 
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. :)
 
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanged mass'

Thread 'A cylinder connected to a hanged mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Coulomb's law to find electric field for charge density function
Replies
11
Views
1K
Conceptual understanding/question of guass and Coulomb’s law
Replies
5
Views
2K
Find the electric field on the surface of a sphere using Coulomb's law
Replies
6
Views
2K
Using Gauss' Law to find the field at a point
Replies
6
Views
1K
Dependence of Coulomb's law on the medium
Replies
8
Views
3K
Electric field at a point inside a non-uniformly charged sphere
Replies
6
Views
1K
Q) Deriving Gauss' Law from Coulomb's Law for a Single Point Charge
Replies
1
Views
2K
Calculating Charge and Force Using Coulomb's Law and Trigonometry
Replies
6
Views
8K
Gauss's Law vs Coulomb's law problem
Replies
3
Views
2K
Ohm's law, current density, free & bound charge
Replies
16
Views
2K

Hot Threads

Recent Insights

Back
Top