# Defining charge

1. Sep 22, 2009

### Surreal Ike

Defining "charge"

Hello folks,

My physics teacher told the class that he was eventually going to give us a pop quiz with only one question: "In one sentence, without any math, what is charge?" I think I know the answer, but since it's going to count for an entire quiz grade, it'd be nice to confirm it.

Anyway, my answer is: "Charge is the difference between the total number of protons in a body and the total number of electrons in a body."

Is that correct? Any suggestions for how I can improve it? One thing I can think of is that in insulators, atoms will sometimes align themselves in one direction or another in a regular fashion. Does that count as charge? Also, my answer kind of contains math, so that might be a problem.

2. Sep 22, 2009

### jambaugh

Re: Defining "charge"

It doesn't sound bad except it may beg the question "what about neutrons"...which means you are just putting off the fact that protons have charge 1e and electrons charge -1e.

I think the best way to define something like charge is to describe how a "charged object" behaves. If I gave you a new type of particle, call it an jambaughon and asked you to figure out if it had a charge then what would you do. This is what is known as an operational definition. It's a definition based on how you observe the quantity or quality to be defined. Since that's what science is all about that's the best form of definition.

3. Sep 23, 2009

### Surreal Ike

Re: Defining "charge"

Operational definitions can be good, but my teacher says when he first gave this question, he threw away all the quizzes in disgust because no one got even close. My guess is that since the operational definition is pretty obvious lots of folks used it and ended up getting their papers thrown away. He would probably say that what you describe are just "properties" of charge and not charge itself.

4. Sep 23, 2009

### Surreal Ike

Re: Defining "charge"

On the other hand, maybe you're right and I'm wrong because quarks also have charge...

5. Sep 23, 2009

### Phrak

Re: Defining "charge"

Charge is the divergence of the electric field, always associated with mass.

6. Sep 23, 2009

### Surreal Ike

Re: Defining "charge"

Sounds like something we're going to learn later in the quarter. What do you mean by "associated with mass"?

7. Sep 23, 2009

### jambaugh

Re: Defining "charge"

Well since the quiz is over. Here's what I think the operational definition of a charge should be:

The electric charge of a particle is the strength with which it interacts with an electromagnetic field.

One could add that two particles may have equal magnitude but opposite effect on and are equally but oppositely affected by EM fields and thus have opposite charge.

One could also add that electric charge is a fundamental conserved physical quantity in current theory.

One problem with my definition though is that it doesn't quite distinguish charge from dipole (and higher multi-pole) moments. But of course that is hard without being definite about the mathematical form of the interactions.

8. Sep 23, 2009

### jambaugh

Re: Defining "charge"

That is charge density and I'd say invoking divergence is "using math" and also ... what do you mean associated with mass?

9. Sep 23, 2009

### Phrak

Re: Defining "charge"

If you write out the classical field equations, charge (density) propagates at c. Maxwell's equations and the Lorentz force are an incomplete set of postulates without constraining charge to mass.

Another answer--electric charge, as well as charge continuity are a direct consquence of applying a 4-vector bundle to a psuedo Riemann manifold and associating with one quanity.

If I were prone to guessing, I'd say a certain professor has a particular way he understands charge, and we're attempting to guess what that is.

Perhaps he's looking for a phenomenological answer as you prefer. Beats me.

Last edited: Sep 23, 2009
10. Sep 24, 2009

### jambaugh

Re: Defining "charge"

But my understanding was that we needn't invoke the mass association a priori but rather it is a consequence of the field energy for the field around the charged particle. (That is qualitative consequence not quantitative.)
Huh? I though one need only append the U(1) gauge fiber to the base manifold? The tangent bundle structure is already there as a mathematical construction.
I think your guess is dead on. I also think asking such a question should be to better understand how the students think before going into the topic (and what needs remediation). Rather than tossing the quizzes he should keep them on file and do post instruction comparison. (Of course he should toss the idea of assigning grades.)