Charge on point charge to create a spark

[chicagobears34]

Homework Statement

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

Homework Equations

F=(k*q1*q2)/r^2
f=Eq

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?

 

[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.

 

[chicagobears34]

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.

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

 

[haruspex]

I don't know how you arrived at

E=7.2x10^6 N/C

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.

The point charge needs to have an energy large enough to move the electron 1.1 cm.

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.

 

[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.

 

[haruspex]

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.

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.

 

[chicagobears34]

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.

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

 

[haruspex]

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

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?

 

[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

 

[haruspex]

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

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?

 

[chicagobears34]

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

 

[haruspex]

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

That's the one.