# How to calculate velocity from the attraction of two charges

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1. Oct 25, 2016

### General Scientist

I need to calculate the acceleration of an proton to a metal plate with a charge of 16 Coulombs(negative charge), 1 meter away. Then I need to calculate the velocity at the moment it passes the plate. Starting Velocity is 0 m/s. What is the velocity and what is the acceleration? This is not homework. When I did this, I got an acceleration of 1.376*1018 m/s2. The velocity is then 1.65891531*109 m/s. Also, how long does it take for the proton to get to the plate.

Last edited: Oct 25, 2016
2. Oct 25, 2016

### Staff: Mentor

Even if it is not homework, it is similar to a homework question, so I moved the thread to our homework question.

How large is the plate and what is its orientation?
How did you get those numbers?
Acceleration won't be uniform. Finding the impact velocity is easier if you consider conservation of energy.

Your calculated speed exceeds the speed of light. Do you think that is realistic?

3. Oct 25, 2016

### General Scientist

That is why I added it. It exceeded the speed of light. the size of the plate is two inches in diameter and there is a hole in the middle that is 1/2 inch in diameter and the electron will go through it.

4. Oct 26, 2016

### General Scientist

Mean to say proton

5. Oct 26, 2016

### Staff: Mentor

Which is impossible - you'll have to consider special relativity for this scenario. Note that there is no way to get 16 C onto such a plate. It would explode within a nanosecond.

6. Oct 26, 2016

### General Scientist

Ok then put 5 coulombs

7. Oct 26, 2016

### Staff: Mentor

Something like Nanocoulombs is more realistic. Maybe 1 µC if we are very optimistic.

8. Oct 29, 2016

### General Scientist

Then a 1 micro coulomb.

9. Oct 29, 2016

### Staff: Mentor

It is your problem, why don't you take 1 µC and see what you get?

10. Oct 30, 2016

### General Scientist

I don't know to calculate it because a washer will not have a uniform field

11. Oct 31, 2016

### Staff: Mentor

An exact solution will need some integral or probably even a numerical solution. You can get some reasonable estimate, however.

12. Nov 4, 2016

### General Scientist

Could you please explain the process of calculating an close approximate

13. Nov 4, 2016

### Staff: Mentor

You can approximate the plate as sphere, calculate the velocity of the incoming particle once it hits the (imaginary) sphere (ideally via energy conservation) and then assume that the particle does not accelerate further afterwards. That approximation should be good within a factor of 2.

14. Nov 12, 2016

### General Scientist

F=ma
F=(k⋅q1⋅q2)/d2