Multiplication and division in physics

[PiRsq]

What does it mean to multiply two physical quantities?

Ie: For electrical potential energy the equation is

Ee=kq1q2/r

Where k=Coulombs constant, q1 and q2 are charges in Couloumbs and r is the distance between the charges

What does it mean to multiply q1 and q2?

[HallsofIvy]

What does it mean to multiply q1 and q2?

Uh, since they are numbers, it means just regular multiplication of numbers!

If you mean "what is the physical significance of their product" (not quite what you asked), I don't know that there is any physical significance to it because I don't believe there is any physical quantity that is just that product.

The physical significance of the entire quantity, Ee=kq1q2/r, is precisely given by the definition of "electrical potential energy". You might be able to determine the physical significance by a "dimensional analysis" of the formula but you would really be asking "what is the physical significance of k".

[PiRsq]

What I meant was what is the physical significance of their product? Sometimes I think of it as if the energy between any two charges depend on both charges. Thus the energy in between the two charges is a 'mixture' of both charges...Is that analogy wrong?

[chroot]

Originally posted by PiRsq
What I meant was what is the physical significance of their product? Sometimes I think of it as if the energy between any two charges depend on both charges. Thus the energy in between the two charges is a 'mixture' of both charges...Is that analogy wrong?
Well, the product of two charges has units of "charge squared," which is not a unit with any physical significance. You're not going to walk around the lab and find a metal sphere with squared charge on it.

As Halls said, the units of k are such that the squared charge cancels, and the final answer that pops out of your equation has units of energy. By itself, however, a quantity with units of charge squared does not have any physical meaning.

- Warren

[Rahmuss]

I'm new to all of this; but love physics, so please excuse my ignorance; but what is the electrical potential energy (not the equation; but the definition)? And why do you get it when you multiply the charges by k and divide by r? What does that really mean? How can you get the electrical potential energy by doing that? And what is it used for? Again, forgive my ignorance. Thanks.
-Mike

[Stingray]

I'll try to give you a little more useful answer. Let's define some axioms that should be obvious:
1) The electric potential energy has to depend on the sizes of both charges: U=U(q1,q2)
2) The energy doesn't care which charge you label 1 or 2: U(q1,q2)=U(q2,q1)
3) If there is only one charge, there's no potential energy: U(q1,0)=0
4) Experimentally, electrostatics is linear. Dealing with many particles is essentially the same as dealing with two: U(q1+q1',q2)=U(q1,q2)+U(q1',q2)

All of these statements have physical meaning, but they imply that U(q1,q2)=cq1q2, where c is some constant (k/r here). So you're right that multiplication is a specific type of mixture.

Rahmuss, do you know what potential energy is (non electric)? If not, I think its too involved to describe here (sorry).

[Rahmuss]

<<<1) The electric potential energy has to depend on the sizes of both charges: U=U(q1,q2)>>> Right
<<<2) The energy doesn't care which charge you label 1 or 2: U(q1,q2)=U(q2,q1)>>> Makes Sense. As long as you're not mixing systems of energy.
<<<3) If there is only one charge, there's no potential energy: U(q1,0)=0>>> Sounds Right.
<<<4) Experimentally, electrostatics is linear. Dealing with many particles is essentially the same as dealing with two: U(q1+q1',q2)=U(q1,q2)+U(q1',q2)>>> Ok. I'll trust you.

All of these statements have physical meaning, but they imply that U(q1,q2)=cq1q2, where c is some constant (k/r here). So you're right that multiplication is a specific type of mixture.

Rahmuss, do you know what potential energy is (non electric)? If not, I think its too involved to describe here (sorry). Yep; but just the basics. I know that an object has PE (V with hamiltonian isn't it?) when it is has a force acting on it (such as an object at the top of a slide with gravity acting on it), and it's the same with particles (just different variables to express similar attributes) with charges. The q+ acting on the q- and vice versa, therefore, there is a potential energy that increases and they get closer. I just don't understand physics like I'd like to. I guess I'm just looking for a deeper meaning.

[StarkyDee]

The energy of a particle or system of particles derived from position, or condition, rather than motion. A raised weight, coiled spring, or charged battery has potential energy. I think of it in biological terms, such as the energy stored for later use has potential-which will be used later as active energy. Correct me if I'm wrong guys, but the biological term would be significantly the same as the physical term potential.

[hey.like]

The phys means are in relations unit some times, naturely, the * ? and another calculation is mean in some concept. but it isn't a unit.
a complete unit mean in phys is important.