Don't Ever Mention "Centrifugal Force" to Physicists

[Dale]

Sorry, I meant this kind of charging by induction.

View attachment 321483
Sorry,

What do you think would be the problem? The only difference in how I would teach it would be in figure (b). I would show current going to ground. That would in fact make it easier to teach.

Electrostatic induction works the same regardless of the sign of the charge carriers. Do you think it is necessary for the grounded conductor to be an electrical wire? Couldn’t it just as well be the ocean or some other grounded electrolyte with positive charge carriers? For that matter the ball could be an electrolyte also.

 

[kuruman]

A conductor is defined by Ohm’s law. No need to discuss electrons. Particularly since not all conductors have mobile electrons.

I did not exactly understand what you meant. I took the above to mean that there is no need to discuss any kind of charge carriers free to move inside a conductor. I see now by your statement

The only difference in how I would teach it would be in figure (b). I would show current going to ground.

that you assert the existence free positive charges inside the conductor. More precisely these would be absences of negative charge (dare I say holes?) which of course should also not be mentioned to students. I'm OK with that. However, how we got to this point considering the title of this thread is a source of wonderment.

 

[sophiecentaur]

but then a smart student would note

A really smart student would appreciate that there is more to the subject than the water analogy would suggest. 'Smart' would imply some ability with Maths and an awareness that 'a physical interpretation' is a false friend. The teacher has responsibility here.

A conductor is defined by Ohm’s law.

Hmmm. 'Ohm's Law' describes how metals behave. I know I'm a voice in the wilderness but the expression R=V/I is only a 'law' when a system behaves linearly; otherwise it is a definition of a handy quantity that is often constant over a range of conditions and which we refer to as Resistance. (Do we call v=s/t the velocity law?)

 

[vanhees71]

While we're at it, let's swap the sign on the electron charge so electron flow matches conventional current!

The most confusing concept is to introduce "conventional current" instead of simply using current density, which is a vector with a magnitude and direction given by the flow of the particles making up the "fluid of charged matter": $\vec{j}=q n \vec{v}$, where $q$ is the charge of the particles ($-e$ for electrons), $n$ the particle-number density, and $\vec{v}$ the fluid-velocity field. Then there's no confusion about the direction of the flow of electric charge and no need for fictitious "conventional currents".

A current is more complicated then current densities anyway, because the sign is not only determined by the flow of the charged medium and the sign of the charges of the particles but also by the arbitrary choice of direction of surface-normal elements of the surface you integrate over to get the current,
$$I=\int_{A} \mathrm{d}^2 \vec{f} \cdot \vec{j}.$$

 

[sophiecentaur]

The most confusing concept is to introduce "conventional current" instead of simply using current density, which is a vector with a magnitude and direction

Problem is that kids minds have already been polluted long before they can grasp vectors or current density. The only safe way is to frown on (you can't 'forbid' these days) using electrons until they are capable of dealing with this stuff.

 

[A.T.]

The only safe way is to frown on (you can't 'forbid' these days) using electrons until they are capable of dealing with this stuff.

"You want electrons? You can't handle the electrons!"

 

[Dale]

However, how we got to this point considering the title of this thread is a source of wonderment.

Yes, we are rather far off topic at this point. But nobody has complained yet so “no harm no foul”

 

[Dale]

'Ohm's Law' describes how metals behave.

Ohm’s law describes how conductors behave. Metals are conductors, but so are electrolytes. I understand your objection to calling it a law. To me that is just a historical accident.

 

[vanhees71]

Problem is that kids minds have already been polluted long before they can grasp vectors or current density. The only safe way is to frown on (you can't 'forbid' these days) using electrons until they are capable of dealing with this stuff.

Hm, but with the fluid picture of electric currents everything gets more transparent. Of course, point particles in classical electrodynamics should be avoided, but fluids are fine and very intuitive.

What I found most confusing was the use of the integral formulation of Maxwell's equations, which seems to be still the standard didactic approach in highschool even today more than 30 years later. For me reading the Feynman lectures which finally introduced me to the local form, was a revelation. Particularly all these sign issues become much more simple. You just have to learn how to orient the boundaries of volumes (surfaces) relative to these volumes (boundary-surface-normal vectors out of the volume) and surfaces (boundary path oriented relative to the sufrace-normal vectors according to the right-hand rule), i.e., as in the standard use for the Gauss and Stokes integral theorems.

 

[anorlunda]

but the expression R=V/I is only a 'law' when a system behaves linearly;

But it is also very useful for piecewise linear analysis in nonlinear regions. When I say "it" I mean not just Ohm's law but KVL, KCL, and all the circuit analysis techniques.

Consider numerical solutions to circuit differential equations. Our main task is to calculate the differential changes in state variables, given the existing states as initial conditions. We can almost always calculate those with the linear methods despite nonlinearities in the components.

 

[kuruman]

The only safe way is to frown on (you can't 'forbid' these days) using electrons until they are capable of dealing with this stuff.

"You want electrons? You can't handle the electrons!"

If you must use electrons "these days", it is imperative to issue a warning before doing so and ask students who might be offended or otherwise distressed to leave the room. Placing such warning in the syllabus is also a good idea although none of these precautions will guarantee your job security if you are an adjunct professor as the recent events at Hamline University indicate.

Sorry for taking the thread farther astray but I had to vent my frustration over this warning thing.

 

[losbellos]

Lol. Hahaha maybe he should have a cable with a mass on it and play with it a bit... Anyways. The fictitious is very wrong word because the radial acceleration obvious even though thats because the mass cannot move circular because of its nature. It has to be forced. So the centrifugal force = force required to keep and object on circular path... (or turn etc) But a simpler calculus is the omage^2 * l * m. So Not a fictitious force because you have to exert against it!!!! It can do damage, change, deformation etc. That it only exists in motion that's something else.

 

[vanhees71]

If you must use electrons "these days", it is imperative to issue a warning before doing so and ask students who might be offended or otherwise distressed to leave the room. Placing such warning in the syllabus is also a good idea although none of these precautions will guarantee your job security if you are an adjunct professor as the recent events at Hamline University indicate.

Sorry for taking the thread farther astray but I had to vent my frustration over this warning thing.

How can innocent particles like electrons be offending? Did I miss someting?

 

[kuruman]

So the centrifugal force = force required to keep and object on circular path...

That is not correct. The force required to keep an object on a circular path must be directed towards the center of the circle. The centrifugal force, as the name suggests, is directed away from the center.

 

[sophiecentaur]

But it is also very useful for piecewise linear analysis in nonlinear regions. When I say "it" I mean not just Ohm's law but KVL, KCL, and all the circuit analysis techniques.

My point is that R is just a ratio - like velocity. There is no Law involved. Sometimes there is a constant R over a range and sometimes there isn't. The term "Ohm's Law" is mis-applied nearly always. Is the Miles per Gallon that you use for your fuel consumption ever called The Consumption Law? Of course not; it's just a ratio. Can you really say that mpg is any less law-like than Volts per amp? People are too locked-in to bring themselves to question it. George Ohm got it right; it's just the later generations that went and spoiled it.
The shame is that, along with a lot of terms and ideas that happen to be used in the context of EE (the worst offender), it's used too early in kids' intellectual development and they take it on board as truth.
And, btw, KVL and KCL are different cases. They are Identities, rather than Laws; they are just smart bits of Maths with no Physics involved in themselves.

 

[anorlunda]

@sophiecentaur , you may be surprised that I agree with you, but only partially. See my Insights article:

Learn Why Ohm’s Law Is Not a Law

Reference: https://www.physicsforums.com/insights/ohms-law-mellow/

 

[waross]

Ohm's Law.
No just a good idea;
It's the law!

 

[waross]

Centrifugal force,
Centripetal force.
Centripedal force. A force that encourages walking.
Nancy "Boots" Sinatra was influenced by this force.

 

[waross]

The best reason to avoid the use of the word "centrifugal" is that use leads to endless futile discussions such as this one.
May I suggest futile?

 

[vanhees71]

One has to understand that the "constitutive laws" we usually learn in the introductory electrodynamics lecture are not fundamental laws but are derived from the fundamental laws in terms of "many-body physics". The best theory we have is, of course, quantum theory, and you can derive the constitutive laws indeed by using quantum-many body theory. For standard household matter (aka electrical engineering purposes) non-relativistic many-body theory will do, and at the ususal linear level what you use is linear-response theory as the most simple approach, i.e., you consider external electromagnetic fields which are much smaller than the intrinsic electromagnetic fields holding the electrons, atomic nuclei/molecules together in your macroscopic piece of matter.

For a piece of metal a simple but not too bad model is the "Jellium Model", i.e., you consider the (conduction) electrons as a gas of negatively charged particles moving in a continuous positive-charge distribution. Astonishingly it's not too bad to even simplify this to treat them as an ideal highly degenerated Fermi gas, and then you can as what happens when I apply an electromagnetic field to the metal. Then you can simplify everything to a magnetostatic or quasistationary approximation, and you'll get out "Ohm's Law",
$$\vec{j}=\sigma \vec{E},$$
where $\sigma$ is a typical transport coefficient, which depends on the material (which kind of metal) and the temperature, i.e., you have an effective macroscopic model, derived from the underlying fundamental microscopic physics. That's what condensed-matter theorists do with great success, and the practical use of such effective models like "Ohm's Law" needs not to be emphasized.

For a very nice presentation of "macroscopic electrodynamics", see Landau&Lifhsitz vol. 8. There they often even use classical models, which are also not too bad. More emphasis on the quantum approach is given in vols. 9 and 10.

 

[losbellos]

That is not correct. The force required to keep an object on a circular path must be directed towards the center of the circle. The centrifugal force, as the name suggests, is directed away from the center.

So they oppose and have the exactly the same values... So it is correct! That in vector it is pointed inwards or outwards that something else, you havent seen that in the equation did you??

 

[kuruman]

I agree with you abut Ohm's, law that it's just a ratio. It probably started at its inception as general rule for different materials and retained its name for historical reasons as more and more "non-Ohmic" materials were discovered.

And, btw, KVL and KCL are different cases. They are Identities, rather than Laws

Here I beg to differ. I would not call them identities but consequences of equations that are based on empirical evidence, laws if you wish.

KVL is a direct consequence of Faraday's "law" in the static case as expressed by Maxwell's equation for the curl of the electric field. It is essentially an energy conservation equation because the electric field is conservative. Formally, starting with Faraday's law when there is no time-varying magnetic field, $$ \mathbf{\nabla}\times\mathbf{E}=0\implies \oint \mathbf{E}\cdot d\mathbf{l}=0\implies -\sum_i\Delta V_i=0.$$ KCL is a result of the "law" of charge conservation which is written as $$\mathbf{\nabla} \cdot \mathbf{J}+\frac{\partial \rho}{\partial t}=0$$ Construct a closed Gaussian surface enclosing any part of the circuit, multiply by a volume element $dV$ and integrate over the volume to get $$\int_V \mathbf{\nabla} \cdot \mathbf{J}~dV+\int_V \frac{\partial \rho}{\partial t}~dV=0.$$ Use the divergence theorem to transform the first volume integral into a surface integral and rearrange to get $$\int_S \mathbf{J}\cdot~\mathbf{\hat n}~dA=- \frac{\partial}{\partial t}\int_V\rho~ dV.$$The left hand side represents the total current coming out of the surface of volume $V$ because $\mathbf{\hat n}$ is the outward normal. If there are $N$ locations on the surface where current comes out, the left hand side can be written as $$I_{\rm{out}}=\sum_{i=1}^{N}\int_{S_i} \mathbf{J_i}\cdot~\mathbf{\hat n}~dA=\sum_i^N I_{\rm{out,i}}$$ The right hand side is the rate of change of the total charge enclosed within the volume. Thus, we write $$\sum_i^N I_{\rm{out,i}}=- \frac{dq_{\rm{encl.}}}{dt}.$$ That's the general form of KCL. We note that

1. When as much current goes into the volume as comes out, the derivative on the RHS is zero and $\sum_i I_{\rm{out,i}}=0$ with the understanding that charge going in the $i$th location on the surface is added as $-I_{\rm{out,i}}$. Of course in this case the other side of the equation is zero so the sign doesn't matter as long as charge out has opposite sign to charge in.

2. The sign does matter when the enclosed charge is changing. Consider, for example, the case of volume $V$ enclosing only the positive plate of a discharging capacitor through resistor $R$. There is only one location where charge can come out, i.e. $N=1$. Then $\frac{dQ}{dt}$ is a negative quantity which makes $I_{\rm{out}}$ positive. The current in the circuit must be drawn from the positive plate to the resistor before applying KVL.

I know I'm not saying anything new here, but it's nice to see that what might be considered "obvious" can be traced back to fundamental equations and principles that apply in general.

Edit: Minor typo fix.

 

[Dale]

So they oppose and have the exactly the same values... So it is correct!

No, your statement was not correct, for the reason pointed out by @kuruman in post 104.

Please do not try to push incorrect physics on this forum. That is not tolerated here. Simply learn and move on.

 

[kuruman]

So they oppose and have the exactly the same values... So it is correct!

In addition to @Dale's comments in post #113, you should realize that you have undermined your own argument if your statement quoted above is correct. When two opposing forces of equal magnitude act on a moving object at the same time, the object cannot move in a circle but in a straight line at constant velocity.

 

[vanhees71]

So they oppose and have the exactly the same values... So it is correct! That in vector it is pointed inwards or outwards that something else, you havent seen that in the equation did you??

You have to clearly distinguish which forces are present in which frames. In the inertial frame of reference there are only "true forces" (i.e., due to interactions, for everyday matter usually electromagnetic and gravitational ones only), i.e., there's a centripetal force, which keeps the particle on its circular trajectory.

In the rest-frame of the particle, i.e., in a rotating non-inertial frame and only in this frame you have the inertial forces in addition.

 

[A.T.]

centrifugal force = force required to keep and object on circular path

No, that would be centripetal not centrifugal.

Centrifugal (inertial / fictitious) force is merely introduced to make Newtons 2nd Law work in a rotating frame of reference.

So they oppose and have the exactly the same values...

Centrifugal (inertial / fictitious) force and centripetal force have the same magnitude only in special cases, not in general.

 

[sophiecentaur]

Here I beg to differ. I would not call them identities but consequences of equations that are based on empirical evidence, laws if you wish.

I agree with you but perhaps only to some extent. I could be wrong but weren't Kirchhoff's 'laws' based on circuits, currents and voltages, originally? At a deeper level, there is a crossover into Maxwell but isn't it true to say that trying to solve for time varying situations actually takes you beyond KVL and KCL? (Shaky results about Induction when used on their own.)
In a practical sense and, for the majority of students, Kirchhoff is a neat trick for solving DC circuit problems.

In as far a KVL: and KCL kick off by using a definition of R and that. along with definitions of Current and Voltage leads to what I would call two Methods, rather than laws. I guess that, in as far as they are Falsifiable propositions, you could say they are scientific laws. (as opposed to "ohms Law" which is only half stated by most of its users.

 

[anorlunda]

using a definition of R and that.

My point of disagreement is that Ohm's law necessitates a range in which R is constant. It works perfectly well where there is no linear range of R.

 

[kuruman]

I could be wrong but weren't Kirchhoff's 'laws' based on circuits, currents and voltages, originally?

I would say so. Experiments with circuit, currents, magnetic needles etc. provided the basis for Maxwell's synthesis that showed how all these are related and can be derived from four equations plus the conservation of charge equation. My objection was to labeling KVL and KCL as "identities". I think "special cases of general principles" would be a more appropriate label.

 

[sophiecentaur]

I think "special cases of general principles" would be a more appropriate label.

Yes - that's fair enough but they are stated in complete terms - unlike Ohm's Law. They don't actually involve explicit resistance.
We are agreeing.