Total electric potential of systems of point charges

[Atomos]

suppose there existed 3 point charges with known charges and separating distances. I know you can determine the total potential of the system by using one charge as a reference (give it a potential of 0J), calculate the potential of another charge with respect to that charge (x J), and then calculate the last charges with respect to both charges (y J), and then the potential would be given as 0 J + x J + y J.

This seems perfectly logical to me, but I can't quite wrap my mind around why calculating the potential with respect to the other two of each charge and then adding is wrong.

 

[quantumdude]

I know you can determine the total potential of the system by using one charge as a reference (give it a potential of 0J), calculate the potential of another charge with respect to that charge (x J), and then calculate the last charges with respect to both charges (y J), and then the potential would be given as 0 J + x J + y J.

That does not give you the total potential energy. It just gives you the potential energy that the first charge sees. To get the total you have to repeat the process for the other two charges and add the results.

See the following web page:

http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter26/Chapter26.html

 

[kyle8921]

I can confirm that your understanding of calculating the total potential of a system of point charges is correct. The potential energy of a point charge is directly proportional to its charge and inversely proportional to the distance between the charges. Therefore, in a system of three point charges, the total potential energy can be calculated by adding the individual potentials of each charge with respect to a chosen reference point.

Calculating the potential with respect to the other two charges and then adding them together would not give an accurate representation of the total potential energy of the system. This is because the potential of a charge is affected by the presence of other charges in the system. By using one charge as a reference and calculating the potential of the other two charges with respect to it, we are taking into account the influence of all three charges on each other.

In summary, your method of calculating the total potential energy of a system of point charges is correct and aligns with the principles of electrostatics. It is important to consider the influence of all charges in the system when determining the potential energy of a specific charge.