Calculating the force between two electrons in a wire

In summary, an infinite line charge with a linear charge density of lambda0 produces an electric field of 5E4 N/C at a distance of 2m. To find the force between two adjacent extra electrons in the wire, the units of lambda are determined to be C/m and it is calculated that there are 6.25E18 electrons per meter. Using Coulomb's law, the meters per electron is calculated to be 2.9E-14 m per electron and the force between the two electrons is determined to be 0.28N.
  • #1
helixkirby
15
0

Homework Statement



An infinite line charge (wire) has lambda = lambda0. It produces an electric field of magnitude 5E4 N/C at a distance of 2m. Determine the typical force between two adjacent extra electrons in the wire

Homework Equations


E_line = lambda/(2pi*r*epsilon0)

The Attempt at a Solution


I managed to find lambda0 using the above equation, but now I'm stuck trying to find the force between the two electrons, how do I find thelectricity e spacing between them given the linear charge density, can anyone help me?
 
Physics news on Phys.org
  • #2
What are the units of λ?
 
  • #3
gneill said:
What are the units of λ?
C/m
 
  • #4
helixkirby said:
C/m
Right. So how many electron charges make up a Coulomb?
 
  • #5
gneill said:
Right. So how many electron charges make up a Coulomb?

1/1.6E-19 = 6.25E18 electrons
 
  • #6
So how many electrons per meter for your value of λ?
 
  • #7
gneill said:
So how many electrons per meter for your value of λ?
epsilon0 * 5E4 *4pi*6.25E18 electrons per meter I believe
 
  • #8
Okay. What's the result of the calculation? What does it tell you about the meters per electron?
 
  • #9
gneill said:
Okay. What's the result of the calculation? What does it tell you about the meters per electron?
I finally got it, I inverted the calculation to get the meters per electron which was about 2.9E-14 m per electron, then used this with coulomb's law to get .28N, thank you so much, my professor was giving me cryptic hints when I emailed him.
 

Related to Calculating the force between two electrons in a wire

1. What is the formula for calculating the force between two electrons in a wire?

The formula for calculating the force between two electrons in a wire is given by Coulomb's law, which states that the 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. Mathematically, it can be represented as F = k(q1q2)/r^2, where F is the force, k is the Coulomb constant, q1 and q2 are the charges of the two electrons, and r is the distance between them.

2. How does the distance between two electrons affect the force between them?

The distance between two electrons has an inverse square relationship with the force between them. This means that as the distance increases, the force decreases, and vice versa. This relationship is because the force acts over a larger area as the distance increases, resulting in a weaker force between the two electrons.

3. What is the Coulomb constant and what is its value?

The Coulomb constant, denoted by k, is a proportionality constant that relates the force between two point charges to their charges and distance. Its value is approximately 8.99 x 10^9 Nm^2/C^2 in a vacuum. The value of k can vary depending on the medium between the two charges, as it takes into account the permittivity of the medium.

4. Can the force between two electrons in a wire be repulsive?

Yes, the force between two electrons in a wire can be either attractive or repulsive, depending on the charges of the two electrons. If the two electrons have the same charge (both positive or both negative), the force between them will be repulsive. On the other hand, if the two electrons have opposite charges, the force between them will be attractive.

5. How does the force between two electrons in a wire affect the wire itself?

The force between two electrons in a wire does not affect the wire itself as the wire acts as a neutral medium for the electrons to flow through. However, the force between the electrons can cause the wire to move or bend if the force is strong enough. This is the principle behind electric motors, where the force between the electrons is used to produce motion in the wire.

Similar threads

Position for maximum electric field between two wires
    • Introductory Physics Homework Help
Replies
10
Views
2K
Force on a particle of a linear charge distribution
    • Introductory Physics Homework Help
Replies
1
Views
787
Calculating the number of electrons given the force of repulsion
    • Introductory Physics Homework Help
Replies
5
Views
3K
Electric field & force due to charged insulating hemispherical shells
    • Introductory Physics Homework Help
Replies
12
Views
179
Electromagnetism: Force between two charged plates
    • Introductory Physics Homework Help
Replies
1
Views
940
I What causes the magnetic force in a uniform magnetic field?
    • Special and General Relativity
Replies
20
Views
1K
Force on Electron in Light Bulb Filament (240V, 6.0cm)
    • Introductory Physics Homework Help
Replies
2
Views
812
Electric force between two equal parallel rings of charge
    • Introductory Physics Homework Help
Replies
9
Views
2K
Coulomb's Law problem: Force of attraction between the two singly charged ions
    • Introductory Physics Homework Help
Replies
3
Views
3K
Electric field of an infinitely long charge carrying wire
    • Introductory Physics Homework Help
Replies
21
Views
3K

Hot Threads

Recent Insights

Back
Top