Coulomb's Law with 3 Point Charges

In summary, the conversation discusses a comment about a situation with three point charges held fixed along a linear line. The statement claims that there will be zero net electric force on the charge in the middle due to the other charges, but the student does not agree. They explain that the forces of the two outer charges on each other are not as important as the forces they generate on the test charge in between them. The force caused by the +Q charge points towards the middle, while the force caused by the -Q charge points away from the middle. Therefore, there will be a net electric force on the charge in the middle, contrary to the statement.
  • #1
alever
9
0

Homework Statement


The questions asks to consider the following comment about a situation where there are three point charges held fixed along a linear line.

"There will be zero net electric force on the charge in the middle due to the other charges. Using Coulomb's law, the force due to the +Q charge is positive, and the force due to the -Q charge is negative. The forces cancel."

It then asks if we agree with the statement, and to explain.


Homework Equations


Since we are dealing with Coulomb's law F=Kq1q2/r^2


The Attempt at a Solution


So there is a positive source charge (+Q) and a negative source charge (-Q) and there is a positive test charge (+q) place in the middle. I don't believe that there wouldn't be a net electric force on the charge in the middle, but I'm having trouble gathering my thoughts, or not sure where to start?
 
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  • #2
alever said:

Homework Statement


The questions asks to consider the following comment about a situation where there are three point charges held fixed along a linear line.

"There will be zero net electric force on the charge in the middle due to the other charges. Using Coulomb's law, the force due to the +Q charge is positive, and the force due to the -Q charge is negative. The forces cancel."

It then asks if we agree with the statement, and to explain.


Homework Equations


Since we are dealing with Coulomb's law F=Kq1q2/r^2


The Attempt at a Solution


So there is a positive source charge (+Q) and a negative source charge (-Q) and there is a positive test charge (+q) place in the middle. I don't believe that there wouldn't be a net electric force on the charge in the middle, but I'm having trouble gathering my thoughts, or not sure where to start?

Homework Statement


Hi alever, welcome to PF.

Draw a diagram with the three charges in place and draw in the vectors representing the forces acting on the test charge in the middle. Which directions do they point? Do they oppose or reinforce?
 
  • #3
gneill, thanks for your quick response. The +Q and -Q will be attracted toward the middle, so their force vectors will point toward each other, and the positive test charge in the middle would be attracted to the -Q charge, is that what you were referring too?


+Q---> +q---> <-----Q

So if I were explaining this do I say "No, I don't agree with the statement, because the positive test charge will have a force vector pointing to the right toward the -Q?"
 
  • #4
alever said:
gneill, thanks for your quick response. The +Q and -Q will be attracted toward the middle, so their force vectors will point toward each other, and the positive test charge in the middle would be attracted to the -Q charge, is that what you were referring too?
The forces of the two outer charges (+Q and -Q) on each other are not so important here. It's the forces they generate on the test charge between them than matters. What is the direction of the force caused by the +Q charge? What is the direction of the force caused by the -Q charge?
+Q---> +q---> <-----Q

So if I were explaining this do I say "No, I don't agree with the statement, because the positive test charge will have a force vector pointing to the right toward the -Q?"
That would be an appropriate answer, yes.
 
Last edited:
  • #5
gneill said:
alever said:
gneill, thanks for your quick response. The +Q and -Q will be attracted toward the middle, so their force vectors will point toward each other, and the positive test charge in the middle would be attracted to the -Q charge, is that what you were referring too? [\quote]
The forces of the two outer charges (+Q and -Q) on each other are not so important here. It's the forces they generate on the test charge between them than matters. What is the direction of the force caused by the +Q charge? What is the direction of the force caused by the -Q charge?
That would be an appropriate answer, yes.

Great! Thanks for your quick help!
 

1. How is Coulomb's Law used to calculate the force between 3 point charges?

Coulomb's Law states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. To calculate the force between 3 point charges, the force between each pair of charges must be calculated using the same formula, and then vector addition must be used to determine the total force acting on each charge.

2. What is the direction of the force between 3 point charges?

The direction of the force between 3 point charges is always along the line connecting the two charges. If all three charges have the same sign, the force will be repulsive and if two charges have the same sign and one has the opposite sign, the force will be attractive.

3. Can Coulomb's Law be used to calculate the force between charged objects that are not point charges?

No, Coulomb's Law is specifically applicable to point charges, which are objects with infinitesimal size and uniform charge distribution. For objects with finite size and non-uniform charge distribution, other methods such as integration must be used to calculate the force between them.

4. What is the unit of force in Coulomb's Law?

The unit of force in Coulomb's Law is Newtons (N). This is because the force between two charges is equal to the product of their charges (measured in Coulombs) divided by the square of the distance between them (measured in meters squared).

5. Can Coulomb's Law be applied to objects with non-static charges?

Yes, Coulomb's Law can still be applied to objects with non-static charges as long as the charges remain constant during the interaction. However, if the charges are changing, then the force between them will also be changing and the law cannot be used to accurately calculate the force.

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