From rest, how fast would two particles be going at the instant they collide ( if they attract) or when they're infinitely far apart (if they repel)? Explain carefully.
Particle A: 3nC
Particle B: -4nC
Each has a mass of 7 mg. They are .05 m apart.
ΔK + ΔU = 0
ΔK = (1/2)mv(f)^2 - (1/2)mv(i)^2
ΔU = Qa(Vb-Va) <--- I used particle A to find the potential energy at the location of particle B.
The Attempt at a Solution
They both start from rest so initial velocity is 0. So the equation I got for the final velocity is SQRT[(kQaQb)/mr]. All I did was added up the kinetic energies of both particles and the electric potential energy of the entire system, which is just those two particles, and set that equal to 0, and solved for final velocity.
So I am assuming that particle B or Qb is a negative charge due to the negative sign, both particles will attract and collide with each other. So the final velocity for both charges the instant they touch or collide with each other is an ERROR. Under that square root, the value is a negative, and you can't really square root a negative.
The reason why I got a negative value under that square root was due to the PE = Q(Vb -Va), where Vb is the electric potential at r=0 (when they touch) and Va at r= .05m apart. Since I can't get a value for the final velocity for attraction, I tried finding the final velocity for when they are really far apart. So in this case, Vb is the electric potential at r = .05 m and Va at r = infinity (when they are far part). By doing this, the negatives cancels out under the square root, giving me a final velocity of 3.8E-6 m/s for when they are really far apart.
Am I overthinking this or did I do something wrong with my algebra here with the equations? Did I set everything up correctly? And if this is on the correct right path, can someone explain to me why I couldn't get a final velocity value for when they collide? Is there any other reasons as to why opposite charges won't attract each other or even have a final velocity at the instant they collide with each other?
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