Coulomb's Law with 3 Point Charges

[alever]

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?

 

[gneill]

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?

 

[alever]

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?"

 

[gneill]

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.

 

[alever]

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!