Well said. Classically, the sources in Maxwell’s equations are ##\rho## and ##\vec J## which are continuous. As far as I know, all of the paradoxes and inconsistencies in classical EM are based on using Dirac delta functions as the sources.f95toli said:you can't (and shouldn't) use these to think about individual charges
Can we only think of them as an ideal gas, thus a continuous medium? What result will go wrong when thinking about individual charges?f95toli said:We can of course use semi-classical models such as the Drude model, but you can't (and shouldn't) use these to think about individual charges.
What's the problem with using direct Delta function at its source?Dale said:all of the paradoxes and inconsistencies in classical EM are based on using Dirac delta functions as the sources.
There are several. The most obvious one is that the field energy is infinite around a point charge. This would lead to point charges being infinitely massive, an infinite amount of energy release as two opposite charges collide, etc.feynman1 said:What's the problem with using direct Delta function at its source?
They respond to an electric field.feynman1 said:How do point charges move along the boundary of the conductor and how do they stop (equilibrium) in the end?
If there is only an electrostatic field, particles can't stop, can theyMister T said:They respond to an electric field.
No, I wasn't asking this question. 2 questions below. I wonder what happens when charges hit the boundary. Do they bounce several times on the boundary or do they just stick to the boundary upon colliding it? How do charges move along the boundary and finally grind to a halt?Delta2 said:If i understand correctly you are asking why the free electrons are not being ejected from the conductor when an external electrostatic field is applied, instead they seem to stop at the surface. This cannot be explained by classical physics, from what I know according to quantum physics the free electrons must be accelerated to a very high velocity in order to be ejected from the conductor.
I think you have some sort of mechanical model in your mind (the electrons being some sort of balls that are bouncing against a solid wall-the boundary) which i don't think is entirely correct. But maybe a more knowledgeable member than me should answer here, maybe @vanhees71 .feynman1 said:Do they bounce several times on the boundary or do they just stick to the boundary upon colliding it
Exactly. I need (wish) a mechanical model with electrons thought of as balls bouncing around, as suggested by the original post (classical).Delta2 said:I think you have some sort of mechanical model in your mind (the electrons being some sort of balls that are bouncing against a solid wall-the boundary) which i don't think is entirely correct. But maybe a more knowledgeable member than me should answer here, maybe @vanhees71 .
feynman1 said:Exactly. I need (wish) a mechanical model with electrons thought of as balls bouncing around, as suggested by the original post (classical).
Why would you want such a thing?feynman1 said:Exactly. I need (wish) a mechanical model with electrons thought of as balls bouncing around, as suggested by the original post (classical).
Classically, on a conductor at DC there is a surface charge density and a volume current density. Both of these are continuous charge distributions classically, not point charges, for the reasons I pointed out above.feynman1 said:I wonder what happens when charges hit the boundary. Do they bounce several times on the boundary or do they just stick to the boundary upon colliding it? How do charges move along the boundary and finally grind to a halt?
The surface charge density produces an internal field such that the current density near the surface has no component perpendicular to the surface. Thus there is no “hitting the boundary” etc.feynman1 said:I wonder what happens when charges hit the boundary. Do they bounce several times on the boundary or do they just stick to the boundary upon colliding it? How do charges move along the boundary and finally grind to a halt?
If the direction of the electric field is opposite to the direction of motion.feynman1 said:If there is only an electrostatic field, particles can't stop, can they
Isn't the work function rather than the surface charge itself that inhibits current density from going perpendicular to the surface?Dale said:The surface charge density produces an internal field such that the current density near the surface has no component perpendicular to the surface. Thus there is no “hitting the boundary” etc.
Even that doesn't mean charges will stop. But they can still bounce around.Mister T said:If the direction of the electric field is opposite to the direction of motion.
No, it is the surface charge. The work function keeps the surface charge from leaving, but it only affects the surface charge density. The surface charges, in contrast, affect the current density throughout the conductor.feynman1 said:Isn't the work function rather than the surface charge itself that inhibits current density from going perpendicular to the surface?
Are you speaking under the context of electrostatics or electrodynamics, with current or without?Dale said:The surface charge density produces an internal field such that the current density near the surface has no component perpendicular to the surface. Thus there is no “hitting the boundary” etc.
I started that post with “on a conductor at DC”. I didn’t want to deal with the messy details of electromagnetic waves and skin depth etc. But of course electrostatics is just DC with 0 current density, so what I said applies there too.feynman1 said:Are you speaking under the context of electrostatics or electrodynamics, with current or without?
Since the surface charge density interacts with the free electrons, so free electrons apply forces to the surface charges, what keeps the surface charges at their place, that is at the surface. Why they do not move to the outside of the conductor or to the interior?Dale said:The surface charge density produces an internal field such that the current density near the surface has no component perpendicular to the surface. Thus there is no “hitting the boundary” etc
I know why they don't move outside of the conductor. That is due to a work function. But I don't know why they can't move back to the interior.Delta2 said:Since the surface charge density interacts with the free electrons, so free electrons apply forces to the surface charges, what keeps the surface charges at their place, that is at the surface. Why they do not move to the outside of the conductor or to the interior?
The bulk of the wire is neutral so there is no force on the surface charge density from the current density.Delta2 said:Since the surface charge density interacts with the free electrons, so free electrons apply forces to the surface charges, what keeps the surface charges at their place, that is at the surface. Why they do not move to the outside of the conductor or to the interior?
Dale said:No, it is the surface charge. The work function keeps the surface charge from leaving, but it only affects the surface charge density. The surface charges, in contrast, affect the current density throughout the conductor.
It may be a bit confusing to try to use Energy and Field in the same argument. You can do it all with Energy by saying the energy to move from place to place within the conductor is a lot lower than the energy to remove charge from it. Water moves easily from place to place in a bowl but it needs a lot of energy to climb up the sides. You can tilt the bowl slightly to displace the water so it can flow into another bowl through a hole just above the surface, which is like a connection to another conductor (If you really want a mechanical approach / analogy.)feynman1 said:I know why they don't move outside of the conductor. That is due to a work function. But I don't know why they can't move back to the interior.
who mentioned energy?sophiecentaur said:It may be a bit confusing to try to use Energy and Field in the same argument. You can do it all with Energy by saying the energy to move from place to place within the conductor is a lot lower than the energy to remove charge from it. Water moves easily from place to place in a bowl but it needs a lot of energy to climb up the sides. You can tilt the bowl slightly to displace the water so it can flow into another bowl through a hole just above the surface, which is like a connection to another conductor (If you really want a mechanical approach / analogy.)
Work Function?feynman1 said:who mentioned energy?
Equilibrium doesn’t mean that mobile electrons ever “stop” in a conductor in a literal sense. In case a dynamical equilibrium is established – the electrochemical potential of the electrons becomes constant throughout the conductor –, currents in one direction are – so to speak –“cancelled” by currents in the opposite direction.feynman1 said:How do point charges move along the boundary of the conductor and how do they stop (equilibrium) in the end?
that's not a kind of energysophiecentaur said:Work Function?
Yes it is, it is the minimum amount of energy needed to move an electron from a solid to the vacuum,feynman1 said:that's not a kind of energy
Yes, sorry I didn't mean to deny it being an energy. I just meant that wasn't 'work' in the usual sense of introductory physics.f95toli said:Yes it is, it is the minimum amount of energy needed to move an electron from a solid to the vacuum,
The clue is surely in the Units involved, rather than a "sense". In the case of Work Function, the name itself associates the Kinetic Energy and the Photon Energy so it's actually quite hard to be confused in the context of Photoelectricity. What we are discussing is not exactly introductory Physics.feynman1 said:Yes, sorry I didn't mean to deny it being an energy. I just meant that wasn't 'work' in the usual sense of introductory physics.