Calculate Min Distance of 2 Electrons Fired at Speed v

  • Thread starter shawshank
  • Start date
  • Tags
    Electron
In summary, the minimum distance that two electrons will reach after being fired at each other can be calculated using the formula 2ke^2 / mv^2 = r. However, it seems that the answer provided in the book may not match this formula. There is also the possibility that the electric potential energy needs to be equal to the combined initial kinetic energies of the two electrons, which would be 2 * 1/2 mv2 = mv2.
  • #1
shawshank
62
0
electron together

2 electrons are fired at speed v towards one another. Knowing that each electron has a charge of e an mass m, what is the minimum distance that the two electrons will reach after fired at one another?

My book has a different answer than me so I have to check with you guys.

I wrote, -dE = dEk

-(E2 - E1) = (Ek2 - Ek1) - Ek2 is zero to for minimizing radius, and we assume E1 to be zero.

E2 = Ek1

2ke^2/r =mv^2

2ke^2 / mv^2 = r

Now in our book, they had this question with numbers, i derived this formula and plugged in my values and it didn't match the answer in the book.
 
Last edited:
Physics news on Phys.org
  • #2
i never get any answers here man :(
 
  • #3
no luck?
 
  • #4
It seems that the electric potential energy is correct, but using conservation of energy, that would have to equal the combined initial kinetic energies of the two electrons, which would be 2 * 1/2 mv2 = mv2.
 

1. How do you calculate the minimum distance between two electrons fired at a certain speed?

The minimum distance between two electrons fired at a certain speed can be calculated using the Coulomb's Law formula, 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.

2. What is the formula for Coulomb's Law?

The formula for Coulomb's Law is F = k(q1*q2)/d^2, where F is the force, k is the Coulomb's constant (9x10^9 Nm^2/C^2), q1 and q2 are the charges of the two electrons, and d is the distance between them.

3. Can the minimum distance between two electrons be greater than 0?

No, according to Coulomb's Law, the force between two electrons is infinite when the distance between them is 0. Therefore, the minimum distance between two electrons must be greater than 0.

4. How does the speed of the electrons affect the minimum distance between them?

The speed of the electrons does not directly affect the minimum distance between them. However, the speed does affect the force between them, which in turn affects the minimum distance. As the speed increases, the force between the electrons also increases, ultimately resulting in a smaller minimum distance.

5. Is there a limit to how close two electrons can get?

According to Coulomb's Law, there is no limit to how close two electrons can get. However, at extremely small distances, the laws of quantum mechanics come into play and can affect the behavior of the electrons. At this scale, the concept of distance becomes less relevant.

Similar threads

Replies
39
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
8K
  • Introductory Physics Homework Help
Replies
9
Views
6K
  • Introductory Physics Homework Help
Replies
11
Views
4K
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
23
Views
286
  • Introductory Physics Homework Help
Replies
6
Views
5K
Back
Top