Calculating Kinetic Energy Using the Work-Energy Theorem

[evgeniy]

Hi there,

I am thinking about a problem here,

A particle q produces an electric potential of 6.30E2 V at a distance of 1 m away. If a particle of charge Q=0.00300 C is released from rest at a distance of 8.00 m from q, what will be its kinetic energy after moving very far from q?

My question is, can I use the work-energy theorem here? As in
Ki + Ui = Kf + Uf ?
If I choose a point at 8.00m, then the Ki will be zero, am I right? Then Ui would be Ui = Vi/Q, is this the right equation to use? And then at infinity or very far away, Uf will be zero too. Is this the right approach?

Need help...thanks in advance

 

[Doc Al]

My question is, can I use the work-energy theorem here? As in
Ki + Ui = Kf + Uf ?

That's conservation of energy: sure you can use it.

If I choose a point at 8.00m, then the Ki will be zero, am I right?

Right. It's released from rest at that point.

Then Ui would be Ui = Vi/Q, is this the right equation to use?

No. U = VQ. But how can you find the potential at 8 m? You are only given the potential at 1 m. (Hint: How does potential from a point charge depend on distance?)

And then at infinity or very far away, Uf will be zero too. Is this the right approach?

Yes.

 

[evgeniy]

I see what you are saying.
I kinda get it now. So I am supposed to find a potential at 8m. But...
using the equation V = U/qo = 1/4(pi)(epsilon-naught) * q/r...r is the distance from the point charge q to the point at which the potential is evaluated right? But I do not know the value of a charge of q. So I need to find a charge first since I know the potential at 1m. And after it, I will find the potential at 8m, since now I know the charge. And at the end I will use U = Vq. Am I correct?

 

[Doc Al]

Yes, you are correct. But don't waste any time calculating the charge. Use ratios! (You know that the potential is proportional to 1/r; that's all you need to know.)