# Find the minimum distance between 2 particles

• Helly123
In summary, the minimum distance between two point particles is when the potential energy is at its maximum and the kinetic energy is at its minimum.
Helly123

## Homework Statement

A point particle of mass m and charge q(>0) approaches to a point particle Q(>0) at a fixed position. When the distance between the two particles is L, the speed of the moving particle is v. The permittivity of the vacuum is denoted as Epsilon0. Find the minimum distance between the two particles?

## The Attempt at a Solution

What i get is, the Q will repel q at the shortest distance q will ever able to reach. Because of the Force between them. So
I used
Vfinal ^2 = Vinitial ^2 -2as

S is the question
a is force/m

Force is kQq/r^2

I know i am wrong.
I don't know what epsilon for..
Please help me..

This is an energy problem. What is the initial potential energy and kinetic energy? And what will be the kinetic energy as the distance is minimized? Hint: What will happen after the distance reaches a minimum? They want you to use MKS units: ## F=\frac{Qq}{4 \pi \epsilon_o r^2} ##, with a related expression for the potential energy.

Helly123
Helly123 said:
I used
Vfinal ^2 = Vinitial ^2 -2as

S is the question
a is force/m

Force is kQq/r^2
You cannot use the eqn ##v^2=u^2+2as## unless the acceleration ##a## is constant. Here the particle experiences a varying force throughout its approach towards ##Q##.
Think of a way you can employ the conservation of energy principle, or find an expression for the velocity of ##q## at an instant as a function of ##r##, the distance between ##q## & ##Q##.

Helly123 and Charles Link
PKM said:
You cannot use the eqn ##v^2=u^2+2as## unless the acceleration ##a## is constant. Here the particle experiences a varying force throughout its approach towards ##Q##.
Think of a way you can employ the conservation of energy principle, or find an expression for the velocity of ##q## at an instant as a function of ##r##, the distance between ##q## & ##Q##.
Yes.. the problem i get is non constant of acceleration. @Charles Link also pointed out important thing for me.

Ek at min distance is zero.
Ep = kQq/r_2
r_2 is the min distance
K = 1/4pi.epsilon0
Ek1 + Ep1 = Ep2 + 0
Solve for r2

Thanks all

Charles Link

## 1. What is the minimum distance between two particles?

The minimum distance between two particles is the smallest distance that can exist between them. It is the closest distance that the two particles can be from each other without touching or overlapping.

## 2. How is the minimum distance between two particles calculated?

The minimum distance between two particles is calculated by finding the distance between their centers or closest points. This can be done using mathematical equations such as the distance formula.

## 3. What factors affect the minimum distance between two particles?

The minimum distance between two particles can be affected by several factors, such as the size and shape of the particles, their charges, and any external forces acting on them.

## 4. Why is finding the minimum distance between two particles important?

Finding the minimum distance between two particles is important in understanding the interactions and forces between particles. It can also help in predicting the behavior and movement of particles in a system.

## 5. Can the minimum distance between two particles ever be zero?

No, the minimum distance between two particles cannot be zero. This would mean that the particles are touching or overlapping, which is physically impossible. The minimum distance is always at least the size of one of the particles.

### Similar threads

• Introductory Physics Homework Help
Replies
5
Views
242
• Introductory Physics Homework Help
Replies
7
Views
190
• Introductory Physics Homework Help
Replies
2
Views
367
• Introductory Physics Homework Help
Replies
14
Views
2K
• Introductory Physics Homework Help
Replies
12
Views
691
• Introductory Physics Homework Help
Replies
1
Views
3K
• Introductory Physics Homework Help
Replies
25
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
932
• Introductory Physics Homework Help
Replies
4
Views
428
• Introductory Physics Homework Help
Replies
3
Views
206