Find the Distance for Net Zero Force: Two Charges at Origin and x=L

[cmcdonald29]

1.)Two charges are fixed in location: charge q1= +8e is located at the origin and charge q2= -2e is located on the x-axis at x=L. At what point can a proton be placed so that it has net zero force acting on it?


2.)F=kq1q2/r^2


3.)I tried to do F=0
K = 8.988 X 10^9 (constant)
q1 = (8 protons) X (1.602 X 10^-19) ---> (individual charge of one proton)
q2 = (2 electrons) X (1.602 X 10^-19)

I used the equation above then to find r^2; however, as you can see F = 0 X r^2 would give me zero and you cannot divide by 0 to find r. I am confused on how to find the distance.

 

[DrClaude]

Hi cmcdonald, welcome to PF!

1.)Two charges are fixed in location: charge q1= +8e is located at the origin and charge q2= -2e is located on the x-axis at x=L. At what point can a proton be placed so that it has net zero force acting on it?


2.)F=kq1q2/r^2


3.)I tried to do F=0
K = 8.988 X 10^9 (constant)
q1 = (8 protons) X (1.602 X 10^-19) ---> (individual charge of one proton)
q2 = (2 electrons) X (1.602 X 10^-19)

I used the equation above then to find r^2; however, as you can see F = 0 X r^2 would give me zero and you cannot divide by 0 to find r. I am confused on how to find the distance.

Don't do plug-and-play with the formulas, think about the problem first.

I suggest drawing a picture to illustrate the situation, and think about the forces that are acting on the proton. Also, can you figure out without any calculation in what region you expect the proton to be: ##x \leq 0##, ##0 < x \leq L##, or ##x > L##?

 

[cmcdonald29]

I would expect the charge to be located on the opposite side of the electron the exact same distance from the origin proton location.

 

[DrClaude]

I would expect the charge to be located on the opposite side of the electron

That's correct.

the exact same distance from the origin proton location.

We'll see about that one after you've solved the equations...

So, put the proton in your drawing and write the formula for all the forces acting on it.

 

[cmcdonald29]

I'm still a bit confused on how to actually approach the problem itself. I don't understand what equations I should be using to get it started?

 

[DrClaude]

The equation you gave in point 2 of the OP.

 

[cmcdonald29]

Yes, but I am confused on how I would plug into the equation as putting a 0 force in with not let me work out any distance.

 

[DrClaude]

F=kq1q2/r^2

That equation is for two charges. What happens when you have three?