Is "R" always positive? (not a HW problem -- it's a general question)

[JoeyCentral]

This references a specific problem in my Physics class in relations to electrical potential and electrical fields, but I kind of want a more general answer in terms of physics. So obviously, I know that distance is always positive. However, when I was given a problem to solve, there were 3 different charges with their own respective charges. This is not really a homework problem since I already know how to use the given information to solve for electric potential and electric field. Long story short, when I was plugging in the numbers, apparently I got the answer wrong for calculating the total charge at a single point because I used a negative number for distance. My physics teacher told me that distance is always positive, but by my mathematical analysis, it looked almost like it was -x distance from the origin (or in this case, the point).

Well, this is a problem that I really need to know, especially if electrical engineering is going to involve a lot of physics like this. I know distance in theory is positive. However, if I was given a formula and the formula had the letter "r" or "R" in it, does that mean that it will always denote a positive number since it is a distance? I am sorry if this is a dumb question, but like I said, I want to make sure I am 100% prepared for engineering school and the only way I can do that is by improving my physics. I am good with the math, but I just want to sharpen that physics a little bit. Thank you!

 

[ZapperZ]

You are confusing the distance between something versus either position or displacement. Those two are not the same.

In cartesian coordinates, the position may have a negative value. However, the distance between something isn't! And object at +3i and another at -3i does NOT have a distance of zero between them if you try to simply add these values, even though the other object is at a "negative position".

Look at what the physics requires.

Zz.

 

[JoeyCentral]

So no matter what position the object is to the point of interest, the difference between the two object's position will always be positive?

 

[jbriggs444]

So no matter what position the object is to the point of interest, the difference between the two object's position will always be positive?

It's a bit more nuanced than that and is the same as the distinction between "speed" and "velocity".

The "difference" (or "displacement") between the positions will be a vector. It can be positive or negative. More generally, it may be in any direction. The "distance" between the positions will always be positive (or possibly zero). It is a scalar and has no direction.

The "distance" between Chicago and Des Moines is about 400 miles. The "displacement" from Chicago to Des Moines is 400 miles West. The "displacement" from Des Moines to Chicago is 400 miles East.

 

[JoeyCentral]

But does the letter R always mean distance in a formula?

 

[jbriggs444]

But does the letter R always mean distance in a formula?

Depends on the formula.

 

[JoeyCentral]

Well I thought about it and I honestly think that distance is always used in formulas. I am not sure if there are many formulas out there that care about displacement unless you were dealing with vectors.