# Electric potential and kinetic energy

1. Feb 20, 2008

### tony873004

1. The problem statement, all variables and given/known data
A point charge Q is fixed in position, and a second object with charge q and mass m moves directly toward it from a great distance. If the initial speed of the object is v, compute the minimum distance between the two objects. If Q=1.0 μC, q=1.0 nC, m=1.0*105 kg, and v= 3.0*105m/s, what is the minimum distance of approach?

2. Relevant equations

3. The attempt at a solution

$$\begin{array}{l} \frac{{kQq}}{{r_1 }} + \frac{1}{2}mv_0^2 = \frac{{kQq}}{{r_2 }} + \frac{1}{2}v_f^2 ,\,\,\,\,\,\,\,\,\,\,\,\,v_f = 0 \\ \\ \frac{{kQq}}{{r_1 }} + \frac{1}{2}mv_0^2 = \frac{{kQq}}{{r_2 }} \\ \\ r_2 = \frac{{kQq}}{{\left( {\frac{{kQq}}{{r_1 }} + \frac{1}{2}mv_0^2 } \right)}} \\ \\ r_2 = \frac{{8.99 \times 10^9 {\rm{N}} \cdot \frac{{{\rm{m}}^{\rm{2}} }}{{{\rm{C}}^{\rm{2}} }}1.0\mu {\rm{C}} \cdot 1.0{\rm{nC}}}}{{\left( {\frac{{8.99 \times 10^9 {\rm{N}} \cdot \frac{{{\rm{m}}^{\rm{2}} }}{{{\rm{C}}^{\rm{2}} }}1.0\mu {\rm{C}} \cdot 1.0{\rm{nC}}}}{{r_1 }} + \frac{1}{2}1.0 \times 10^{ - 5} \cdot 3.0 \times 10^5 } \right)}} \\ \end{array}$$

This reminds me somewhat of gravity's escape velocity problem, where your final distance is irrelevant as long as it is large (theoretically infinity).

How do I dismiss r1, the initial starting position in this problem? Can I just get rid of the entire first term in the denominator, since when r1 is large, it approaches 0?

Thanks!

**edit, 3*105 should be (3*105)2. I get 2*10-11 meters for the answer. Did I do this right?

Last edited: Feb 20, 2008
2. Feb 20, 2008