# Relationship between electric energy and force

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1. Feb 26, 2015

1. The problem statement, all variables and given/known data
One of the three types of radioactive decay is "β decay", during which protons decay into neutrons or viceversa, emitting either electrons (β) or positrons (β+) at high velocity as a result. In one experiment, a β source and β+ source are placed 10 cm apart from each other. At a certain time, both sources decay simultaneously, with the electron being emitted along the xaxis and the positron being emitted along the yaxis (i.e. the paths of the two particles are at a right angle). Both particles are emitted with 5 keV(kiloelectron volts) of kinetic energy and start on the xaxis. What is magnitude and direction of the total force on each particle? (Do not ignore electric force, assume electrons and positrons have the same mass.)

2. Relevant equations
ΔE=Ui+Uf=−∫F.dr=>F=−∇E

3. The attempt at a solution
I attempted to solve this using conservation of energy. Initially, we have both kinetic and potential energy. Kinetic energy is given to us and we can find electric potential energy. I'm assuming the total final energy (kinetic + potential) is zero since Vf = 0 and Uf = 0 (since distance between the two particles gets "infinitely" long). I then tried to use the equation

ΔE=Ui+Uf=−∫F.dr=>F=−∇E

But I'm not sure how this would help. I feel like I'm missing something. The fact that the question states "don't ignore electric force" makes me think I have to use it, but then if I'm using the electric force formula what's the point of having the initial energy? Any help would be appreciated.

2. Feb 26, 2015

### BvU

I have a hard time imagining what is described here. Are these e+ and e- shot off away from each other, or towards each other ?

And why do you think the final energy would be zero ? There's 10 keV of energy and energy can be converted into other forms, but it doesn't just go away.

(There's also 1020 keV/c2 of rest mass -- a big POOF if the two happen to meet) .

3. Feb 26, 2015

The charges are moving away from each other. This is all the question states, there aren't any other information given. But apparently it's supposed to be a fairly straightforward calculation...

4. Feb 26, 2015

### BvU

WEll, I didn't pick that up from the wording

So you have two opposite charges, 10 cm apart. What's to stop you from calculating the electric force between them ?

5. Feb 26, 2015

Nothing is stopping me from calculating the electric force, I'm just not sure why the kinetic energy is given. This chapter is about potential and potential energy so I have to use those somehow...

6. Feb 26, 2015

### BvU

I see what you mean. You feel some obligation towards the sadist that thought up these exercises, eh

So why the blabla about e+ and e- and not, for example two pea shooters instead of these scary radioactive sources ?
What would be the force on each of the peas given they have a kinetic energy of 16 GeV each ? ( approx 0.1 gram at 5 m/s )