Hi, I am solving a E&M problem and it led me to a conceptual question about comparing voltages. If I measure from ground to,say, three points. I get the values 1v, 5v, and -5v. Which do I consider the minimum, am I taking the absolute value? Thanks in advance.
In mathematics, the module or the absolute value of a real number x, denoted |x| is the actual number taken without sign (thus, for example, number 5 is the absolute value of 5 and -5). Making an analogy with the electrical, things are the same. And if I were to take into account your example, the minimum value will be 1V (because I taking the absolute value).
I am not questioning which would be minimum if I used absolute values, but rather whether one should use absolute values. In other words, when we compare voltages do we use the magnitude of the potential or the number itself?
It depends on the purpose of what you are doing. If you are asking which has the lowest potential, then you use the algebraic minimum. One way to get at this is to consider that you could have measurement them with respect to any other node -- you didn't have to use ground. So what would you have gotten if you had measurement them relative to something that was at -10V? What would you have gotten had you measured them relative to +10V? Then ask if, for your purpose with regards to the question you are answering, if you should get the same answer for which has the minimum voltage regardless of which node you choose to measure them?
While mathematically -5 is less than +1, -500 volts can be fatal, +20 not likely. I would go with the -5
I am trying to determine the point of minimum potential between to fixed charges. So I used the E field created by both at some point r on the shared axis with the origin placed at the first charge where d is the distance between the charges. Next I took the derivative of E with respect to r. Finally I set equal to 0 to find the point of maximum Efield,then I figured that since E and V are related with opposing signs the max E is the min V??..
If you are looking for a point of minimum potential between two charges, then you are (almost certainly) looking for the minimum of the absolute value.