Acharge of 3.20 μc is held fixed at the origin. a second charge of 3.20 μc is released from rest at the position (1.25 m, 0.570 m).
a) if the mass of the second charge is 2.63 g , what is its speed when it moves infinitely far from the origin? (m/s)
b) at what distance from the origin does the second charge attain half the speed it will have at infinity?

a) and b)

Explanation:

We have to analyze this problem from the point of view of energy conservation. In this case there are two kind of energy, electric potential energy and kinetic energy. First, at there isn't relative movement between the two charges, so kinetic energy is zero and the total energy () is just potential.

where is the Coulomb constant, and are the two interacting charges, and is the distance between them.

Considering the fixed charge at (x1,y1) = (0,0) and the second one at (x2, y2) = (1.25, 0.57), the initial distance is

, then if

and   ,

.  

Now, at ,  and . This means all the energy is kinetic

, so

(mass in Kg).

That would be the velocity when the second charge moves infinitely far from the origin.

For the second part we have that , so kinetic energy is

and potential energy is

so the distance is