posted by Steve on .
Two identical +9.5uF point charges are initially 3.5cm from each other.
If they are released at the same instant from rest, how fast will each be moving when they are very far away from each other? Assume they have identical masses of 2.0mg
Here is one way to do this.
I assume you are in calculus. Lets pretend we can do this charge by charge.
work done=INT force dx from x=.03 to inf
integrate it over that domain of x.
So that is the energy this partical has.
Now, with the first charge is gone, the second charge doesn't move.
So the total work in the system is what we figured on the first charge. So if both particles were released, this energy would have been divided evenly, so now we know the KE of each particle
KE=1/2 work done above
1/2 m v^2=1/2 work done above
solve for v
I am not in calculus. Is there any other way to to this through algebra?!
calculate potential energy when close to each other.
You probably have the formula which Bob Pursley just told you how to derive with calculus by integrating the force
it is something like
U = k Q1 Q2 / R
The (1/2)m v^2 of each particle is half of that