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I tried to in detail, explain what creates the high voltage in a Van de Graff generator. But I got problem doing that.

Van de Graaff generator:

First some background of a Van de Graaff generator, there is a comb that is "combing" a rolling belt to create and transfer charge away to create a voltage in a ball shaped metal encasing.

More info about the whole process can be found here: https://en.wikipedia.org/wiki/Van_de_Graaff_generator

My contradiction

Though, I never understood what creates the super high voltage (1 million volt) of a Van de Graaff generator? And an argument that contradicts the high voltage creations of a Van de Graaff generator is that the energy required to remove an electron of an atom(ionization energy) is just a few eV(around 5eV - 30eV). Assuming the voltage of this system is the same as the voltage required to remove an electron. Then, a Van de Graaff generator can only generate the same voltage as the voltage needed to remove one electron from the atom, (i.e. a few volts)?

I'm a bit reluctant on accepting that the voltage is proprtional to the amount of charge of the Van de Graaff generator, because voltage is always relative (Energy/Charge). It's like saying a battery can generate few million volts because it can carry a lot of charge.

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    $\begingroup$ Van de Graaff generators indeed create high voltages by mechanically transporting charge from ground to the terminal. Why is this difficult to visualize? If you stacked a million batteries you would have a high voltage. If you move lots of charge across, in essence, a capacitor you will make a high voltage. My accelerator lab does it every day... $\endgroup$ – Jon Custer Mar 26 '17 at 16:34
  • $\begingroup$ And existing ones go much higher than 1 MeV. Some go higher than 20 MeV. $\endgroup$ – jmh Jun 26 '17 at 14:31
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This is how it works:

van der graaf

vdgr

So there exists a power supply that provides the positive charge and removes the electrons. The comb is for distributing the charges.( Depending on the materials used one could accumulate negative charges and remove the positive ones)

The Concentration of Charge

It is important to realize that the charge on the roller is much more concentrated than the charge on the belt. Because of this concentration of charge, the roller's electric field is much stronger than the belt's at the location of the roller and lower brush assembly. The strong negative charge from the roller now begins to do two things:

It repels the electrons near the tips of the lower brush assembly. Metals are good conductors because they are basically positive atoms surrounded by easily movable electrons. The brush assembly now has wire tips that are positively charged because the electrons have moved away from the tips, toward the connection at the motor housing.

It begins to strip nearby air molecules of their electrons. When an atom is stripped of its electrons, it is said to be plasma, the fourth state of matter. So we have free electrons and positively charged atoms of air existing between the roller and the brush. The electrons repel from the roller and attract to the electronless brush tips while the positive atoms attract to the negatively charged roller.

The positively charged atomic nuclei from the air molecules try to move toward the negatively charged roller, but the belt is in the way. So now the belt gets "coated" with the positive charge, which it then carries away from the roller.

One should not confuse high voltage with high power. The video shows that it is not dangerous to be charged by a Van de Graaff generator.

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A Van de Graaff generator produces high voltages by charging a (spherical) capacitor with capacitance $C$ by mechanical transport of electric charges into the sphere. So, in principle, according to the capacitor equation $$V=\frac{Q}{C}$$ you should achieve unlimited high voltages by transporting more and more charge into the capacitor. This is, however, limited by the charge leakage currents from the capacitor, which is primarily due to the conductivity of the air which increases due to impact ionization of the air molecules in the high electric fields at the surface of the sphere and can also lead to spark discharges.

High voltages (on the order of thousands of volts) applied to a metal are usually not able to extract electrons (ionize metal atoms) because the surface energy barrier (work function) of only a couple $eV$ is not significantly affected by the electric field which cannot penetrate the metal due to the surface charge. However, at very high voltages leading to very high surface fields the (triangular) surface energy barrier becomes so thin that electrons can quantum mechanically tunnel out of the metal. This is called electron field emission (Fowler-Nordheim tunneling). Thus even if you had your spherical capacitor in vacuum you would get a limitation of the maximum achievable voltage of the generator by charge leakage due to electron field emission.

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The large sphere at high voltage of the Van de Graaff generator acts like a Faraday cage. Inside the sphere is an equipotential if there is no charge inside it. If I bring a single charge q from outside this sphere to inside, once it gets inside the sphere it experiences only a very small force that will attract it to the surface of the sphere. The action of bringing the charge inside the sphere has raised its potential energy. If the sphere is at an electrostatic potential V, then the energy needed to bring the charge q to the surface of the sphere is qV. It takes a little more energy to move from the surface to inside the sphere. Even if V is millions of volts, the force on a single electron in this process is very tiny, so the motors driving the belt that carries the charges in can easily supply it. They will have to work just a little bit harder when the belt is carrying charge though to overcome this Coulomb barrier. It's important that the belt be an insulator so that the charge on its surface can't migrate in response to the electric field produced by the Van de Graaff sphere as the charge moves inside.

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