# Challenging problem of electrostatics

1. Dec 17, 2004

### salman_upright

hi.

Suppose we have one moving electron ,approaching towards a fixed electron.
If they 1mm apart when the moving electron has the velocity of 1000cm/s.
How far will be the moving electron from the fixed electron when it comes to the rest.

mass of electron=9.1E-31 Kg
charge of electron =1.6E-19 C

2. Dec 17, 2004

### Tide

HINT: Energy is conserved!

3. Dec 17, 2004

### dextercioby

Though the problem is absurd (it assumes the electrons as bowling balls,one of them being fixed (probably some "intelligent"dude stuck it with glue :tongue2: )) as (probably) implies electrostatic interaction when it actually ain't,i'll say that the answer can be found out applying the old famous energy conseration law,since that old & tired looking Coulomb potential comes from a conservative force .

Daniel.

4. Dec 17, 2004

### Tide

Hmm. 1 esu, 1000 cm/s, 1 mm - does that suggest to you that radiation, quantum, relativistic and space warping effects are significant? Get back to us when you've carried out the calculation to 137 signficant digits.

5. Dec 17, 2004

### dextercioby

U got me there,Tide... But at least it shouldn't have called them "electrons",but "electrically charged bowling balls".And should have given reasonable figures for mass and charge.

Daniel.

PS.I knew QED only stopped at 12 significant digits. :rofl: IIi guess u saw me a relative of Super(machine gun :rofl: )man...

6. Dec 18, 2004

### salman_upright

don't be smart ok
give me the solution man

7. Dec 18, 2004

### Tide

Well, first, you should be posting your homework problems in the homework section and, second, you should be telling us exactly what YOU have tried so far on the problem. I think it's a bit over the top to DEMAND a solution to YOUR problem from people who give freely of their time and knowledge. Moreover, you've already been given the key hint to actually solving the problem yourself.

8. Dec 18, 2004

### GCT

The moving electron should have a initial kinetic energy. This kinetic energy will need to be dissipated by electromotive repulsion, EMF. Should be easy enough.

9. Dec 19, 2004

### Andrew Mason

$$U_i + KE_i = U_f + KE_f$$

$$KE_i = \frac{1}{2}m_ev^2$$

$$KE_f = 0$$

$$U_i = \frac{kQ_e^2}{d_i}$$

$$U_f = \frac{kQ_e^2}{d_{min}}$$

So:

$$d_{min} =\frac{kQ_e^2}{kQ_e^2/d_i + \frac{1}{2}m_ev^2}$$

$$d_{min} =\frac{d_i}{1 + \frac{d_im_ev^2}{2kQ_e^2}}$$

Plug in the numbers and what do you get?

For $$kQ_e^2$$ I get 23.04E-29 Jm
For $$\frac{1}{2}m_ev^2$$ I get 4.55E-29 J.

So I would say that there is something wrong with the question if the answer is .5 mm.

AM