How to calculate velocity from the attraction of two charges

[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.

 

[mfb]

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?

 

[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.

 

[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.

Mean to say proton

 

[mfb]

It exceeded the speed of light.

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.

 

[General Scientist]

Ok then put 5 coulombs

 

[mfb]

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

 

[General Scientist]

Then a 1 micro coulomb.

 

[mfb]

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

 

[General Scientist]

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

 

[mfb]

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

 

[General Scientist]

Could you please explain the process of calculating an close approximate

 

[mfb]

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.

 

[General Scientist]

What about using these formulas
F=ma
F=(k⋅q₁⋅q₂)/d²
V=√(V₀²+2ad)

 

[mfb]

The acceleration and distance won't be constant. Conservation of energy is by far the easiest approach.