# Charge on point charge to create a spark

1. Nov 2, 2013

### chicagobears34

1. The problem statement, all variables and given/known data
Suppose a free electron in air is 1.1cm away from a point charge. What minimum charge must this point charge have to cause a breakdown of the air and create a spark?

I already have the Electric field and force, which I solved to be
E=7.2x10^6 N/C
F=1.2x10^-12 N
2. Relevant equations
F=(k*q1*q2)/r^2
f=Eq

3. The attempt at a solution
I tried using F=kq1q2 / r^2 and plugging in .011m in as r and then using q1=q2=charge of electron.
Then I did F=Eq and solved for q but i did not get the correct answer.
How should I be approaching this problem?

2. Nov 2, 2013

### hjelmgart

Well, what type of course is this? Electromagnetism or quantum mechanics? I think there are several ways to confront this problem, but it kinda depends on which course it is. Besides a free electron in air is kinda wrong.

The air between the electron and the charge represents some potential energy barrier. The point charge needs to have an energy large enough to move the electron 1.1 cm.

Now I don't understand how you calculated the electric field, though. It seems you need to use Coulombs law, which includes the charge of the point charge as well?

You should use the electrostatic potential energy to solve this, I think.

3. Nov 2, 2013

### chicagobears34

This class is just physics II and should just be a Coulomb's law problem, but I'm not sure what other ways to approach the problem other than the way I already tried

4. Nov 2, 2013

### haruspex

I don't know how you arrived at
The field will depend on the magnitude of the point charge.
Presumably the point charge is positive. On the face of it, it's just a question of whether the field exceeds the breakdown strength of dry air (3.3*106 N/C). But that's for rounded surfaces, so I don't know how it applies here.
There is no minimum field for that, the electron will surely drift into the +ve point charge. The question is whether the field strength is sufficient to break down the air dielectric, generating a cascade of electrons long before the free electron can travel the distance.

5. Nov 2, 2013

### chicagobears34

this was a 4part question and the previous parts solved for the acceleration, force, and electric field.
The parts usually needed variables from the previous part to solve the answer. I got the field and force right and I figure they might need to be used to solve for the charge needed to spark, which was why I included them.

6. Nov 2, 2013

### haruspex

But this part asks you to find the value of the charge that will have a certain consequence, and the strength of the field will depend on that charge, so whatever field you previously calculated cannot be relevant.
Maybe you should post all the parts.

7. Nov 3, 2013

### chicagobears34

Part A:
The average distance an electron travels between collisions is 2.0μm . What acceleration must an electron have to gain 2.3×10^−18J of kinetic energy in this distance?
a=1.3x10^8 m/s^2

Part B:What force must act on an electron to give it the acceleration found in part A?
F=1.2x10^-12 N

Part C: What strength electric field will exert this much force on an electron? This is the breakdown field strength. Note: The measured breakdown field strength is a little less than your calculated value because our model of the process is a bit too simple. Even so, your calculated value is close.
E=7.2x10^6 N/C

8. Nov 3, 2013

### haruspex

OK, that makes it clearer. So the field you calculated is the field you need to generate from the point charge at a source of electrons to generate a spark. So, what point charge will produce this field at the given distance?

9. Nov 3, 2013

### chicagobears34

Do I maybe set Kqq/ r^2 = Eq and solve for the q? We never covered the material in class yet, but the homework was assigned. Not exactly sure what other equations relate r with q other than kqq/r^2

10. Nov 3, 2013

### haruspex

The charge of the electron is not relevant. If you have a point charge q, what is the field strength at distance r from it?

11. Nov 3, 2013

### chicagobears34

oh I found one equation E=kQ/d^2
could that be it?

12. Nov 3, 2013

### haruspex

That's the one.