Is the solution correct? (forces between 3 charged particles)

[PhysicsTeacher159]

Homework Statement

Three charges are arranged in a li ne with 2.5 cm between them, as shown in Figure 2.33. What is the force exerted on a Charge 2 by the other two charges?

Relevant Equations

Coulomb's law

 

[etotheipi]

Well it depends on what you mean by "total". If you define "total" to be the sum of the magnitudes, then it's fine. But that definition is not really helpful, for anything. It's certainly not how I would interpret it.

It's much more common for "total" to mean the vector sum, or equivalently if you write those vectors in terms of a basis, the sum of the components of a particular basis vector.

In that case, if you for instance let the $\hat{x}$ basis vector point to the right, the $x$-component of the resultant force is going to be $F_x = F_{12} - F_{32}$. This is now a useful quantity, which you can use to e.g. determine the instantaneous acceleration.

 

[PhysicsTeacher159]

Thanks.

 

[Gordianus]

Does the worked example come from an "official" book? I can't believe how the "author" ignores the vector nature of forces.

 

[PeroK]

Thanks.

To add to what @etotheipi said: if the forces $F_{12}$ and $F_{32}$ were equal and opposite, then the total force on $q_2$ would definitely be zero. You definitely need a minus sign.

Note that the electric field is what determines the force on $q_2$. There is no sense in which you can add the magnitude of electric fields - they must be added vectorially.

 

[hutchphd]

I am reminded of the chapter from "Surely Your Joking..." where Prof Feynman is approving high school texts for the school board and one problem asks for the sum of the temperatures of four stars. Equivalently cringeworthy calculation.

 

[kuruman]

The directions of the arrows representing F₁₂ and F₃₂ are correctly drawn but with their tips at the charge instead of their tails. Grasping at straws, I can hypothesize how one might look at the drawing and erroneously conclude that since one charge "squeezes" q₂ from the left and the other squeezes from the right, charge q₂ is squozen from both sides with a "total" force that is the sum of the two forces because it should be a harder squeeze than if either force alone acted on the charge. Something like that but still indicative of poor understanding of what a net force and Newton's 2nd are all about.

I also lament the lack of units in the answer.