Electrostatic Force and Coulomb's Law

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Homework Help Overview

The problem involves determining the position of a third charge in an electrostatic setup where two charges are given, one positive and one negative, and the goal is to find a location where the net electrostatic force on the third charge is zero. The context is within the subject area of electrostatics and Coulomb's Law.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the setup of the problem, including the distances involved and the forces acting on the third charge. There are attempts to express the forces in terms of the variables defined, and questions about the correct placement of the third charge are raised.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem setup and the relationships between the charges. Some guidance has been offered regarding the formulation of forces acting on the third charge, but there is no explicit consensus on the solution yet.

Contextual Notes

There is a noted constraint regarding the one-dimensional nature of the problem, as well as confusion about the distances calculated for the third charge, which suggests that assumptions about placement and distances may need further clarification.

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Homework Statement


A charge of 6.00 x 10-9C and a charge of -3.00 x 10-9C are separated by a distance of 60.0 cm. Find the position at which a third charge, of 12.0 x 10-9C, can be placed so that the net electrostatic force on it is zero.


Homework Equations


Coulomb's Law


The Attempt at a Solution


I drew a diagram and I believe that the third charge should be place on the end next to the -3.00 x 10-9C charge. How do I solve for the distance/location of this charge?
 
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This question belongs in the introductory physics forum.

Let

x = distance from the negative charge to the third charge
d = distance between the positive and negative charges
q1 = positive charge
q2 = negative charge
q3 = third charge.

In terms of the variables:

What's the magnitude of the force on the third charge due to the negative charge?
What's the magnitude of the force on the third charge due to the positive charge?
What's the magnitude of the net force on the third charge?
 
So you set the magnitude of q1 on q2 equal to the magnitude of q3 on q2 and solve for the distance (d-.6)?
 
No. For one thing, d is equal to 0.600 m. It's the distance between the positive and negative charges.

(q1=+6.00 nc) <---------------- d=0.600 m ----------------> (q2=-3.00 nc)

You're trying to find x, the distance between the negative charge and the third charge, which I haven't shown in the diagram. Can you indicate where you think the third charge goes?
 
(q1=+6.00 nc) <---------------- d=0.600 m ----------------> (q2=-3.00 nc) -------->(q3)
 
I would get something like that, but I must have fudged my numbers somewhere because I get that it needs to be 3.8m away from q1 and 2.7m away from q2. That wouldn't work as that's more than 0.6m difference, and one needs to keep the problem 1D, else we'll get a net force in the y axis.
 
What's the magnitude of the force on q3 due to q1 in terms of q1, q3, d, and x?
What's the magnitude of the force on q3 due to q2 in terms of q2, q3, d, and x?

Once you have those, you want to sum the forces and set the total equal to 0. You'll have an equation where the only unknown is x.
 

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