What is the final velocity of two point charges moving away from each other?

AI Thread Summary
Two identical +10uC point charges, initially 5.5 cm apart and released from rest, will move away from each other due to their mutual repulsion. The work done on each charge is calculated using the formula W = kqQ/r, resulting in a total energy of 16.3454 J. When far apart, this energy converts to kinetic energy, but since both charges share the energy equally, each has half, leading to a final velocity of 4.1 x 10^3 m/s. The discussion clarifies that the speeds of the charges remain equal as they have identical masses, and any difference in charge values would not affect their velocities unless their masses differ. Understanding this division of energy is key to solving similar problems involving multiple charges.
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Homework Statement



2 identical +10uC point charges are initially spaced 5.5cm from each other. If they are released at the same instant from rest, how fast will they be moving when they are very far away from each other? Assume they have identical masses of 1.0mg.

Homework Equations



Maybe... W=Fd=qEd=qV=0.5mv^2

The Attempt at a Solution



initially,
W=qEd
=kqQ/r
=8.99*10^9*(10*10^-6)*(10*10^-6)/0.055
=16.3454

when they are very far apart,
W=0.5mv^2
=0.5*10^-6*v^2
=16.3454

v=(16.3454*2/10^-6)^0.5
=5717ms^-1

but the real answer is 4.1*10^3ms^-1...
 
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Since both charges are released, each carries W/2 kinetic energy at a large distance. Dividing your result by sqrt(2) gives the correct speed.
 
But how do you know that each charges only carries W/2 KE?
I don't quite understand that...
 
Your problem states that both charges are released simultaneously. They fly apart from each other, and since they are identical, Newton's laws enforce that they will move equally. The total potential energy W that you calculated therefore divides evenly between them.
 
Oh, I got it!
So if the charges are, for example +10uC and +20uC, then the velocity of charge (+10uC) would be v=(W/3*2/10^-6)^0.5, right?
 
No, the speeds differ only if the masses differ. The force each feels is the same regardless of charge because every action has an equal and opposite reaction (remember that one?) but the lighter particle will accelerate more (F=ma).
 
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