Tedious Algebra- Is it needed? - Coulomb Force

[Gamma]

Hello,


A typical problem assigned to students is where there are two charges on the x-axis and find the location of a third charge so that the net force on it is zero or some other force value given. I am wondering what is the idea behind this problem? It can get really complicated when trying to solve this. Or is there another way to solve it easily? Here is an example:

A 3 uC charge is at the origin, a -5 uC charge is at +0.2 m. Find the location of an +8 uC charge so that the net force on the 8 uC charge is -7 N


We can place the 8 uC charge on the negative side say at x m from the origin.
Then we can find the net force on 8 uC and then set it to - 7 N.

This is what I am getting.

-3 /x^2 + 5/(x+0.2)^2 = - 97.2

 

[bschwartz]

I think the main reason for these types of questions is to test students understanding of electrostatic forces and the interaction between differently charged particles. After this type of problem is introduced, the 3rd charge is generally then placed somewhere above or below the other two charges so that now x and y forces have to be taken into consideration. I'm sure this is to test students ability to break down the net force into its x and y components and add them respectively. Yes, it can be a lot of algebra, but it does help to develop a students overall understanding of these forces and principles.

 

[ehild]

These problems help the students to understand the vector nature of Coulomb force. When the charges are along a straight line, the students have to decide where the third charge can be, and use different equations in the different domains.
In your problem, the third charge can be either at x<0 or x>0.2 m. You took only the first case into account.

ehild

 

[Gamma]

Right, we could place the charge on the other end also. To give a complete solution, students have to solve both of these scenarios.

The students that am teaching are extremely challenged in math, so I don't assign them these type of problems. If I assign them, I might ask them to derive the equation and stop short of solving it. I just could not take the muttering that goes on the next day in the class.

 

[ehild]

The equations assigned to problems "where is the force zero on the third charge" is easy to solve.

The students learn that Coulomb force is "F=kQ1Q2/r^2", and are confused both by the direction of F and the meaning of "r" when there are two forces from two charges. You need to remind them the wording of the Coulomb Law "The force is inversely proportional to the square of the distance between the point charges", so they have to use the distance D for "r".
Such problems also help them to understand what is the distance between two points placed at given coordinates and how to define the position of a point charge. You said "We can place the 8 uC charge on the negative side say at x m from the origin". That can confuse the students as they get a positive number although x, as coordinate, is negative. It is better to say "at distance D1 from the first charge" and "at distance D2 from the negative charge" and they need to understand that Di=|x-xi| where xi is the position (coordinate) of the i-th charge.

ehild