Coulomb's law and a voltage frame of reference

[Zeranin]

The amp meter is saturating as you suspected. Need to calibrate at 1 amp current then move away  from the sensor until it reads 10 m amp . By marking that distance as times X100 much like a X10 scope probe. With this in place I should be able to measure the magnetic current.

Actually that won’t work. You completely change the whole geometry one you move the magnet away from the jaws, or don’t have the jaws properly closed. You are correct in saying that the equivalent surface current of your magnets is around 2000 amps, and that is way too high for your current clamp meter to measure, and that’s all there is to it.

Electrons moving in opposite directions where the two edges of the monopole cube touch should run into each other , scattering , now and then. If this happen the electrons will have to radiate a photon from a change in velocity or direction. That would be free energy. Can not have free energy so something must be stopping it or if it does happen the magnet is demagnitized to even the score energy wise. I remember you hinting at this saying the edges touching could damage the magnets. If it does happen then it should spit out a photon now and then. I wonder if it could be measured?

You misunderstand. What I meant to say was that a permanent magnet (PM) behaves as if there was a sheet of current moving around the outside surface, and thus it can be modelled in that way. That said, there is not literally a sheet of current flowing through the material, if there was then it would get very hot from I^2R heating! Ferrites are modelled the same way, but they are not even electrically conductive in the bulk material. Re demagnetization, if you place any PM in a powerful field that pushes the flux in the opposite direction, then you may demagnetize the PM. NdFeB is fortunately very difficult to demagnetize (and also difficult magnetize, but that’s another story) so in practice I doubt that you would demagnetize the individual magnets if assembled into a perfect ‘monopole cube’, but you would be giving the magnets a ‘hard time’.   

Speaking of energy conservation I have an unrelated question. You design then perfect ion accelerator for NASA making sure the ion stream never hits the electrostatic accelerator electrode. If the accelerator electrodes is never hit by an ion then we do not need a power supply to keep it at 10 K volts . All we need is a condenser charged to 10 K volt and our ion accelerator engine will run for years until we run out of ions. Is this not a violation of energy laws?? 

An excellent question, damn you! I need to do some ‘real work’ right now, but I’ll get back to you. I feel like I’m monopolizing the thread – anyone else care to comment on this intriguing question?   

[IanB]

Speaking of energy conservation I have an unrelated question. You design then perfect ion accelerator for NASA making sure the ion stream never hits the electrostatic accelerator electrode. If the accelerator electrodes is never hit by an ion then we do not need a power supply to keep it at 10 K volts . All we need is a condenser charged to 10 K volt and our ion accelerator engine will run for years until we run out of ions. Is this not a violation of energy laws?? 

An excellent question, damn you! I need to do some ‘real work’ right now, but I’ll get back to you. I feel like I’m monopolizing the thread – anyone else care to comment on this intriguing question?

Take the simplest possible charged particle, an electron, and follow it (conceptually) through a closed cycle. The electron starts out at the generator and is accelerated towards the target, picking up energy as it goes. When it hits the target it loses some energy, but it is now in close proximity to the accelerator electrode and thus within its field. Our electron now has to be taken on a journey back to the generator to repeat the cycle. To do this, the electron has to be moved away from the accelerator electrode, against the attractive force that accelerated it on the first part of its journey. Moving the electron in this direction back to the starting point requires work to be done on the electron that balances the energy acquired by the electron when it was accelerated. Thus, energy is conserved.

[John Heath]

The magnet has a 3 m hole and 20 m on the outside with thickness of 3 m .

That's a bloody big magnet! 

Should have said 3 mm not 3 m . Yes  a 30 m magnet would be rather large. Would not fix in a shirt pocket.

[Zeranin]

Take the simplest possible charged particle, an electron, and follow it (conceptually) through a closed cycle. The electron starts out at the generator and is accelerated towards the target, picking up energy as it goes. When it hits the target it loses some energy, but it is now in close proximity to the accelerator electrode and thus within its field. Our electron now has to be taken on a journey back to the generator to repeat the cycle. To do this, the electron has to be moved away from the accelerator electrode, against the attractive force that accelerated it on the first part of its journey. Moving the electron in this direction back to the starting point requires work to be done on the electron that balances the energy acquired by the electron when it was accelerated. Thus, energy is conserved.

All true. The classic example is the old CRT based TV. You have an electron 'beam current' that strikes the phosphor and, as you rightly say, the EHT power supply provides the beam current. The power supplied by the EHT supply is the EHT voltage (10's of kV) multiplied by the beam current. All very straightforward. As you say, the EHT current is in a closed loop.

However, John is thinking about the much trickier case of an ion-thruster, where the 'ion beam' is shot out the back of the spacescraft, and thus never collected by an electrode, quite unlike the case of a CRT where the beam electrons are collected by the phosphor electrode and returned to the EHT power supply. Much trickier situation indeed.

[CatalinaWOW]

However, John is thinking about the much trickier case of an ion-thruster, where the 'ion beam' is shot out the back of the spacescraft, and thus never collected by an electrode, quite unlike the case of a CRT where the beam electrons are collected by the phosphor electrode and returned to the EHT power supply. Much trickier situation indeed.

Spacecraft thrusters do shoot a beam out the back.  In many (maybe most) cases they shoot an electrically neutral beam consisting of both electrons and positively charged ions.  By doing this they avoid accumulating charge on the spacecraft which has a number of benefits.  One of which is eliminating the ever increasing "escape velocity" and associated reduction in propulsion efficiency which occurs when you allow charge to accumulate.

[IanB]

As a thought experiment, I would like to imagine an "iron thruster" mounted to a wheeled cart of some kind. This thruster would have a hopper of small iron balls and a system of permanent magnets to accelerate the balls to high velocity. By suitable arrangement of the mechanism, balls would be fed from the hopper, accelerated by the magnets, and ejected out the back of the cart, thus propelling it forwards. Since the thruster is using permanent magnets, no energy input would be required to propel it as long as the supply of balls remains.

I do not think such an iron thruster can be constructed. I suspect therefore, that the equivalent "zero power" ion thruster cannot be constructed either.

[Zeranin]

Spacecraft thrusters do shoot a beam out the back.  In many (maybe most) cases they shoot an electrically neutral beam consisting of both electrons and positively charged ions.  By doing this they avoid accumulating charge on the spacecraft which has a number of benefits.  One of which is eliminating the ever increasing "escape velocity" and associated reduction in propulsion efficiency which occurs when you allow charge to accumulate.

All true, but see my reply to IanB.

[Zeranin]

As a thought experiment, I would like to imagine an "iron thruster" mounted to a wheeled cart of some kind. This thruster would have a hopper of small iron balls and a system of permanent magnets to accelerate the balls to high velocity. By suitable arrangement of the mechanism, balls would be fed from the hopper, accelerated by the magnets, and ejected out the back of the cart, thus propelling it forwards. Since the thruster is using permanent magnets, no energy input would be required to propel it as long as the supply of balls remains.

I do not think such an iron thruster can be constructed. I suspect therefore, that the equivalent "zero power" ion thruster cannot be constructed either.

A permanent magnet powered iron thruster eh? I like it, and we agree that it cannot be built. However, no one has really answered Johns question. If the ions, or electrons, or both are not actually collected on an electrode (as in a CRT) then how can there be a current flowing on the accelerating electrodes, in which case there is no electrical power needed to run the system. That's what John is asking, and it's a cute question.

Let me ask a similar question. As you know, CRTs have a ‘control grid’ so that the electron beam can be turned on and off, indeed, that is how they create an image. OK, start with the electron beam turned off, so there is no electron beam, and no current being drawn from the EHT supply. Now turn on the beam for just a few microseconds, just long enough to release a dense bunch of electrons. The electron bunch will be accelerated towards the phosphor anode, so make no mistake, work is being done in accelerating those electrons. However, the electrons do not touch and are not collected by any electrode, or the phosphor, while they are in transit, so there can be no electrode or  EHT phosphor current until the electron bunch actually strikes the phosphor, so during this time there is no energy being provided by the electrical power supplies.

Question. Where does the energy come from to accelerate these electrons, while they are in transit, before they strike the phosphor anode? The grey matter is pleasantly tickled.

[John Heath]

Speaking of energy conservation I have an unrelated question. You design then perfect ion accelerator for NASA making sure the ion stream never hits the electrostatic accelerator electrode. If the accelerator electrodes is never hit by an ion then we do not need a power supply to keep it at 10 K volts . All we need is a condenser charged to 10 K volt and our ion accelerator engine will run for years until we run out of ions. Is this not a violation of energy laws?? 

An excellent question, damn you! I need to do some ‘real work’ right now, but I’ll get back to you. I feel like I’m monopolizing the thread – anyone else care to comment on this intriguing question?

Take the simplest possible charged particle, an electron, and follow it (conceptually) through a closed cycle. The electron starts out at the generator and is accelerated towards the target, picking up energy as it goes. When it hits the target it loses some energy, but it is now in close proximity to the accelerator electrode and thus within its field. Our electron now has to be taken on a journey back to the generator to repeat the cycle. To do this, the electron has to be moved away from the accelerator electrode, against the attractive force that accelerated it on the first part of its journey. Moving the electron in this direction back to the starting point requires work to be done on the electron that balances the energy acquired by the electron when it was accelerated. Thus, energy is conserved.

I see your point. However in the case of an ion accelerator the ion never returns to put the energy back into the accelerator gun. This means the ion accelerator gun must lose a tiny bit of energy every time an ion is accelerated into space .

[John Heath]

My solution  for the energy conservation problem for an ion accelerator space ship is to point a finger at where the energy is. If I say the energy is in the concentration of positive charges in the bag of ions to accelerate the ship not the accelerator gun then we are okay. Entropy had to go down to have a bag of ions. If I bust the bag of ions they will spread out in all directions causing entropy to go up.  Same applies to a CRT . What business does an electron have going 30 percent c in the middle of a CRT tube if it did not hit the accelerator first anode and is yet to hit the 32 K volt second anode? Neither first nor second anode have been discharged yet Mr electron has the energy to accelerate to 30 percent c. My guess is the energy came from increasing the entropy of the vacuum in the CRT by adding 1 negative electron charge to a vacuum that is decidedly positively charged to 32 K volts.

Great PEA rendering . I am getting better at predicting what it will look like. I had the middle part right but goofed up the outside . I was sure the field attenuation would be more round but it turned out to be more of a square with round edges.

Mr monopole has been reduced is size from 2 inch square to 1 inch square. A second monopole is on its way that will complement the first , north facing out and south facing out.  It is a given that there will not be an attractive force between the + and - monopoles but have to verify.

Another unrelated thought. In the 2 dimensional infinite resistor problem 2 pi pops up if a resistors square is measured diagonally. If the outside of the resister matrix is terminated properly to simulate infinity then the diagonal measurement should be pi to the last digit. If true then the formula to calculate the termination resisters would be the first time anyone in the history of man has ever derived ip to the last digit from math alone. This would raise a few eye brows in the mathematicians camp.   

[Zeranin]

Great PEA rendering . I am getting better at predicting what it will look like. I had the middle part right but goofed up the outside . I was sure the field attenuation would be more round but it turned out to be more of a square with round edges.

Like you, I expect that if we modelled out further that the mod B contours would start to look round.

Mr monopole has been reduced is size from 2 inch square to 1 inch square. A second monopole is on its way that will complement the first , north facing out and south facing out.  It is a given that there will not be an attractive force between the + and - monopoles but have to verify.

Yes and no. Because it is difficult to accurately build a 'monopole', especially using round magnets, you will not get zero field outside of the cube, though it will be less than for a single magnet alone. The cube with the S poles facing outward will have a total of 6 'South Poles', but will also have 6 North poles - you can see this clearly on the FEA vector plot. Therefore, you will be able to get your to monopoles to weakly attract or repel, depending on their relative orientation.

[IanB]

Question. Where does the energy come from to accelerate these electrons, while they are in transit, before they strike the phosphor anode? The grey matter is pleasantly tickled.

In a CRT a large potential difference is created between the anode and the cathode, producing a strong electric field. It takes a power input to charge up this field, and once in place it stores energy. When electrons travel from the cathode to the anode they are accelerated through the potential gradient created in the field, drawing energy from it, and upon striking the anode they discharge it a little. If we continued without providing a replenishing current between the anode and cathode to keep it charged up the system would become discharged and would stop working. The power input to store potential energy in the electric field is where the energy comes from to accelerate the electrons.

[RIS]

Question. Where does the energy come from to accelerate these electrons, while they are in transit, before they strike the phosphor anode? The grey matter is pleasantly tickled.

In a CRT a large potential difference is created between the anode and the cathode, producing a strong electric field. It takes a power input to charge up this field, and once in place it stores energy. When electrons travel from the cathode to the anode they are accelerated through the potential gradient created in the field, drawing energy from it, and upon striking the anode they discharge it a little. If we continued without providing a replenishing current between the anode and cathode to keep it charged up the system would become discharged and would stop working. The power input to store potential energy in the electric field is where the energy comes from to accelerate the electrons.

now thats a very nice explanation I like it  and that would be nice and a closed system
but I wonder Why is the outer glass of the CRT has a charge.
I mean that is a technical problem but I somehow see some interaction between the closed and open systems.
so What would be a good explanation or opinion for that

[Zeranin]

Question. Where does the energy come from to accelerate these electrons, while they are in transit, before they strike the phosphor anode? The grey matter is pleasantly tickled.

In a CRT a large potential difference is created between the anode and the cathode, producing a strong electric field. It takes a power input to charge up this field, and once in place it stores energy.

Yes. We can go further, and calculate the stored energy from E=0.5CV^2, where 'C' is the stray capacitance between the electrodes to which the EHT power supply is connected. So far, so good.

When electrons travel from the cathode to the anode they are accelerated through the potential gradient created in the field, drawing energy from it, and upon striking the anode they discharge it a little.

Well yes, but what I actually asked was where the energy came from to accelerate a small bunch of electrons, before they strike the anode.

If we continued without providing a replenishing current between the anode and cathode to keep it charged up the system would become discharged and would stop working.

We all agree with that, but here you are presumably referring to the steady state situation, where electrons are returned to the anode, and then ‘pumped’ back to the cathode by the EHT power supply. My question was, where does the energy come from to accelerate a single bunch of electrons, while they are in transit, before  they strike the anode.

The power input to store potential energy in the electric field is where the energy comes from to accelerate the electrons.

That does not really answer the question. Creating the accelerating electric field in the first place is a one-off. Thereafter the electric field strength (V/m) is constant, and does not ‘wind down’ while the bunch of electrons is in transit. Does anyone disagree that the only place that the energy can come from to accelerate our bunch of electrons while in transit is the EHT power supply. Thus the question becomes, how can current be drawn from the EHT power supply during this transit time, when the bunch of electrons does not touch and is not collected by any electrode?

Of course, we all understand how the EHT power supply provides the current and power to accelerate CRT electrons when there is a constant electron beam current, but that was never my question.

My question relates to the case where the CRT control grid is used to produce a small bunch of electrons, that are then accelerated towards the anode. We all understand that once this bunch of electrons strike the anode, then the EHT power supply will need to provide a small pulse of current (and thus energy) to pump those electrons back to the cathode, but that also has nothing to do with my question.

What I am asking, is where does the energy come from to accelerate a single bunch of electrons, while they are in transit, before they strike the phosphor? I have put forward the proposition that the only place this energy can come from is the EHT power supply, which means that current would need to be drawn from the supply during the transit time. Assuming you agree with this, how can such a current exist, given that during transit, the electrons do not touch and are not collected by the anode or any electrode. It’s a fair question, and as yet we have no answer. Where is Catalina to WOW us with the answer?

[IanB]

What I am asking, is where does the energy come from to accelerate a single bunch of electrons, while they are in transit, before they strike the phosphor? I have put forward the proposition that the only place this energy can come from is the EHT power supply, which means that current would need to be drawn from the supply during the transit time. Assuming you agree with this, how can such a current exist, given that during transit, the electrons do not touch and are not collected by the anode or any electrode. It’s a fair question, and as yet we have no answer. Where is Catalina to WOW us with the answer?

Firstly, the electrons left the cathode before they started on their journey. Since the electrons carry charge, they discharged the cathode a little at this point.

Next, the electrons are accelerated through the electric field towards the anode, gaining energy as they go. Since the electrons in motion form an electric current, the moving electrons are actually creating a magnetic field. In this process, some potential energy from the electric field is being converted to stored energy in the magnetic field around the electrons. As the electrons are accelerated, the electric field is weakened (by whatever minuscule amount). Given sensitive enough measurements, the potential difference between the anode and the cathode while the electrons are in transit could be observed to be decreasing. It is as if an inductor has been connected in parallel with a capacitor and some energy is transferred from the capacitor to the inductor.

It might be imagined that the voltage on the capacitor remains constant during the journey of the electrons and drops suddenly when the electrons strike the anode. But this will not be found to be the case. What will be found is that the potential difference remains the same at the moment the electrons leave the cathode, it will then drop gradually as the electrons are accelerated, and it will stop dropping once the electrons strike the anode.

(It might be asked what happens to the stored energy in the magnetic field created by the fast moving electrons? Since there is no recovery path for this energy, it will be dissipated on the collapse of the magnetic field as heat (from eddy currents) and low energy radiation.)

[Zeranin]

What I am asking, is where does the energy come from to accelerate a single bunch of electrons, while they are in transit, before they strike the phosphor? I have put forward the proposition that the only place this energy can come from is the EHT power supply, which means that current would need to be drawn from the supply during the transit time. Assuming you agree with this, how can such a current exist, given that during transit, the electrons do not touch and are not collected by the anode or any electrode. It’s a fair question, and as yet we have no answer. Where is Catalina to WOW us with the answer?

Firstly, the electrons left the cathode before they started on their journey. Since the electrons carry charge, they discharged the cathode a little at this point.

Next, the electrons are accelerated through the electric field towards the anode, gaining energy as they go. Since the electrons in motion form an electric current, the moving electrons are actually creating a magnetic field. In this process, some potential energy from the electric field is being converted to stored energy in the magnetic field around the electrons. As the electrons are accelerated, the electric field is weakened (by whatever minuscule amount). Given sensitive enough measurements, the potential difference between the anode and the cathode while the electrons are in transit could be observed to be decreasing. It is as if an inductor has been connected in parallel with a capacitor and some energy is transferred from the capacitor to the inductor.

It might be imagined that the voltage on the capacitor remains constant during the journey of the electrons and drops suddenly when the electrons strike the anode. But this will not be found to be the case. What will be found is that the potential difference remains the same at the moment the electrons leave the cathode, it will then drop gradually as the electrons are accelerated, and it will stop dropping once the electrons strike the anode.

(It might be asked what happens to the stored energy in the magnetic field created by the fast moving electrons? Since there is no recovery path for this energy, it will be dissipated on the collapse of the magnetic field as heat (from eddy currents) and low energy radiation.)

Hi Ian,
I’m glad you find the problem of sufficient interest to think about it, and you clearly understand that there is a ‘mystery’ here, that requires explanation.

One thing is not clear about your reply. In a CRT system, the cathode-to-anode voltage is fixed, this being the EHT supply voltage, and all my discussions have been on that basis. However, you seem to be considering the case where there is no EHT power supply as such, but only a capacitor to maintain the cathode-to-anode potential, is that correct? Assuming that you are in fact considering the case where there is no EHT power supply, I believe that your posting is largely correct, but still incomplete.

It has taken me a while to reach my own conclusion about the exact correct explanation, but FWIW I finally feel confident in my understanding, so will relate it here. I will describe the situation with a fixed-voltage EHT supply between anode and cathode.

Firstly, the electrons left the cathode before they started on their journey. Since the electrons carry charge, they discharged the cathode a little at this point.

Usually the cathode is at ground potential, connected to mother Earth via the mains ground wiring, so the cathode potential won’t actually change after squirting out a bunch of electrons. In any event, we have a fixed voltage between anode and cathode, and this is the only thing that matters as far as the electric fields inside the CRT are concerned, so our analysis need not be concerned with the fact that our bunch of electrons came from the cathode.

It is true that moving charge produces a magnetic field, and also true that accelerated charge produces EM radiation, but both these effects are very small, and in my view have nothing to do with the true explanation of what is going on, and consideration of either is certainly not necessary to explain what is going on, so I will leave magnetic and EM effects out of the discussion altogether.

We agree that energy is required to accelerate our bunch of electrons while in transit, and I proposed that the only place that this energy could come from is the EHT power supply, and I maintain this is the case. During transit, current is drawn from the EHT supply, even though the anode-cathode voltage remains constant, and even though the moving electron bunch never contacts the anode or any electrode.  Furthermore, there is not a pulse of EHT current when the electrons actually strike the anode.

The question then, is how can current be drawn from the supply, when the electrons are in transit, and not touching or collected by the anode or any other electrode?

The explanation is subtle, and is concerned with the movement of charge (ie a current) through induction. As the electrons approach the anode, they attract positive charge (or repel electrons, same thing) to the anode, as per Coulomb’s Law. The only way that additional positive charge can get to the anode is from the EHT supply, so that is exactly what happens, current flows from the EHT supply to the anode. As the electrons get closer to the anode, they attract still further positive charge, with the result that there is a constant flow of current from the EHT supply to the anode, for the entire time that the electrons are moving from cathode to anode. The relationship Q=CV is in effect maintained at all times, except that Q includes a contribution from the moving bunch of electrons. As the electrons get closer to the anode, they increasingly ‘neutralize’ some of the +ve charges on the anode, and so additional +ve charge has to flow from the EHT supply to the anode, to compensate. By the time the electrons are only a tiny distance from the anode, about to strike it, the total negative charge that has flowed from the anode to the EHT supply is exactly equal to- ve charge about to strike the anode, as must be the case to maintain Q=CV, where Q is the net charge consisting of the charge on the anode, and the moving charge that is just about to strike the anode. Thus, when the moving electrons actually strike the anode and are absorbed into it, there is no pulse of anode current because Q=CV is already satisfied, and the EHT current to the anode that has been present for the entire electron journey ceases. At all times, all the equations of Physics are satisfied, and at all times during the transit and acceleration of the bunch of electrons, current is being drawn from the EHT supply, to provide the power for accelerating the electrons. Everything adds up. If it did not, then I would not sleep at night.

[IanB]

One thing is not clear about your reply. In a CRT system, the cathode-to-anode voltage is fixed, this being the EHT supply voltage, and all my discussions have been on that basis. However, you seem to be considering the case where there is no EHT power supply as such, but only a capacitor to maintain the cathode-to-anode potential, is that correct?

Yes, I realized after the fact that I didn't define the basis of my system model very well. I had in mind the earlier question about the ion thruster, where the electrode once charged up was isolated. By analogy, I considered the case where the anode and cathode of the CRT were charged up by the EHT supply and then the supply was disconnected, so that only the stray capacitance remained to maintain the potential difference (and in my perfect world there are no leakage currents to allow the charge to drain away).

The interesting question to me then became, what would happen to the potential difference between anode and cathode during the time the bunch of electrons were accelerated from cathode to anode? I concluded that the potential difference would gradually decrease since the only source of energy to accelerate those electrons is the energy stored up in the electric field of the capacitance between anode and cathode. The electrons acquire energy, so another part of the system must lose energy to balance it. The only source of that energy is the electric field accelerating the electrons, and nature will not be denied; ergo the field energy must be depleted and the potential difference must decrease.

It is then a small step to conceptually reconnect the EHT supply and observe that it will replace the lost charge in the stray capacitance by supplying some current.

During transit, current is drawn from the EHT supply, even though the anode-cathode voltage remains constant, and even though the moving electron bunch never contacts the anode or any electrode.  Furthermore, there is not a pulse of EHT current when the electrons actually strike the anode.

This I also concluded, as evidenced by my statement here:

It might be imagined that the voltage on the capacitor remains constant during the journey of the electrons and drops suddenly when the electrons strike the anode. But this will not be found to be the case. What will be found is that the potential difference remains the same at the moment the electrons leave the cathode, it will then drop gradually as the electrons are accelerated, and it will stop dropping once the electrons strike the anode.

The gradual drop in potential difference across the stray capacitance if isolated would correspond to the gradual supply of current from the EHT supply during transit if it were connected.

[Zeranin]

We are in complete agreement, IanB.    That's the great thing about science and engineering. After sufficient thought and discussion, agreement is always reached.

[John Heath]

Great posts guys. I'm liking the electron slowly changing the high voltage in transit for the CRT.

The + and - 1 inch square monopole are complete. They are acting as predicted. They will not stick to each other nor a fridge. This is good.

However the complementary monopoles should have acted like an electron and positron. This did not happen? Special relativity predicts this so where is my voltage difference. I feel cheated or more likely I have misunderstood something , story of my life. However I do have an indication that the elusive voltage is there when placing a round magnet on the screen of a TV set. When north or south pole are facing the screen there is a marked black ring where there is a void of electrons hitting the phosphor . Outside and inside the round magnet is okay but not on the edge which is where the electrons should be moving. I have a picture of it.