Elementry Electrostatics question

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Homework Help Overview

The problem involves two point charges, one positive and one negative, placed along the x-axis, and seeks to determine the position of a third charge where the net electrostatic force on it is zero. The subject area is electrostatics, specifically focusing on the forces between point charges.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss setting up the forces acting on the third charge as a function of its position and equating them to find a solution. There is also exploration of the expected location of the third charge in relation to the other two charges.

Discussion Status

Some participants have provided guidance on how to set up the equations for the forces acting on the third charge, while others have raised questions about the correct interpretation of the roots obtained from the equations. There is an ongoing exploration of the implications of choosing different roots in the context of the problem.

Contextual Notes

Participants note the importance of understanding the setup of the problem, including the positions of the charges and the assumptions regarding the location of the third charge. There is a mention of potential confusion regarding which root to select based on the assumed position of the third charge.

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Homework Statement


Two point charges (q1=+20 nC and q2=-40 nC) are placed 10.0 cm apart onlong the x-axis. Where can a third charge (q3=+20 nC) be placed so that the net electrostatic force on that charge is zero?


Homework Equations



F=k(q1q2)/r^2

The Attempt at a Solution



It's definitely not a hard problem, I'm guessing I'm supposed to set the entire equation into equilibrium. Other than that basic concept, I really don't understand how to solve for this problem. My professor only went over calculating forces between two charges.

Thanks for any help, I could really use it. :(
 
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Place q1 at x=0 and q2 at x=10, and put q3 at x=a. Now write the two forces on q3 as a function of a, set them equal and solve for a. It's helpful when you do this to figure out what portion of the line you expect q3 to be on first. Will a<0, 0<a<10 or a>10?
 
So if I'm understanding you correctly, it should look like this:

k*(q1q3)/a^2=k*(q2q3)/(10+a)^2 since a < 0. I think...

So we get a = 4.14

To test this, I can calculate the force between q1 and q3 and match it with q2 and q3, since they should be equal.

So, k*(q1q3)/(4.14^2) = 23.31k
and k*(q2q3)/(10-4.14)^2=23.31k.

Should be correct. Any errors?

Thanks.
 
Careful! I think you are picking the wrong root. You want solve k*(q1q3)/a^2=k*(q2q3)/(10-a)^2 if a<0 is the coordinate of the point. If you solve that you get 4.14 and -24.14. Since you assumed a<0 the one to pick is -24.14. If you call a the distance of the point from the origin then you solve k*(q1q3)/a^2=k*(q2q3)/(10+a)^2 and assuming a>0. You get -4.14, 24.14 and pick the positive one.
 
Ah, ok, I understand. I wasn't sure which root to choose for. Thanks a lot!
 
838 said:
Ah, ok, I understand. I wasn't sure which root to choose for. Thanks a lot!

The root you chose corresponds to the point between the charge at x=0 and the charge at x=10. Here the magnitude of the forces are equal, but they point in the same direction.
 

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