# Why does vacuum have resistance?

1. Dec 10, 2015

### iampaul

Suppose that there is a positively charged particle and a negatively charged particle in free space. The electric field of the positive charge causes a difference in potential between the position of the negatively charged particle and the positively charged particle. This, causes the negatively charged particle to move towards the positive charge without resistance (i think???). Couldn't that be considered as an electric current.
Now, if the source of potential difference is a battery, free space is said to have high resistance, so no current can flow. Why can't the electrons just move towards the positive electrode of the battery? Why does free space have resistance?

2. Dec 11, 2015

### sophiecentaur

There is no need to worry here. Your model is not "free space". There are (your) mobile charges around that can carry the current so we are not dealing with a pure insulator. There is nothing to stop the charges moving around and the rate at which they accelerate is proportional to the Electric Field (Volts per metre).
There is also a problem about using the term 'Resistance' here. You are describing what is basically a transient effect so you would really have to consider the total Impedance of the system, rather than just the Resistive part. [Edit: you have what is effectively a discharging capacitor with some additional dynamics; not straightforward in circuit terms.]
If you are referring to the 'Resistance' of a vacuum gap, then that is different. Firstly, it is not a linear situation because a certain Strike Voltage is needed before electrons are torn off the cathode to allow conduction. Then the Resistance of the gap will be very low, (and not constant) due to the ions in the arc.

Last edited: Dec 11, 2015
3. Dec 12, 2015

### iampaul

Thanks. Haha, I didn't realize that.

4. Dec 12, 2015

### mrspeedybob

I'd like to pose a related question...
Suppose we have charged particles suspended in a vacuum in a circuit configuration. For example, electrons inside a glass torus. The torus is negatively charged so as to repel the electrons and keep them away from the walls. Inside the torus, all gasses have been removed so that it only contains electrons. If this torus was subjected to a changing magnetic field, would it act like a superconducting ring? If not, what force would impede the flow of electrons around the inside?

5. Dec 12, 2015

### sophiecentaur

You are describing something like a cyclotron or a magnetron here. There are many variations of electron beams, flowing in a vacuum and being bent and focussed by electric and magnetic fields. There is a problem in keeping a beam of electrons together because they mutually repel. There is no electric field inside a charged tube and in most electron beam devices, the beam is focussed and guided by magnetic fields.
There's another very basiuc problem here.too. Assuming you could get your beam. going round in a circle, you have another problem and that is the beam will radiate EM because you have charges being constantly accelerated (circular motion). That is a mechanism for energy loss which would stop it being superconductive. The beam would slow down and fall into the wall of the tube unless some more energy were used in changing the magnetic field to correct this.
Electrons (etc.) are little devils to control and keep in a small space - a fact that the seekers after Nuclear Fusion are plagued with.

6. Dec 12, 2015

### mrspeedybob

Why don't the cyclotron radiation effects resist the current flow in a superconducting loop? Or for that matter, make the resistance of any conductor higher when curved.

7. Dec 12, 2015

### sophiecentaur

Good question - take a merit point - but I think I have the answer: The mean acceleration of the electrons is low when the drift speed is less than 1mm/s and the radius is 1m and the frequency of the radiation is in the order of <0.3mHz (a period of more than an hour) so the radiation resistance is very low / immeasurable(?).

8. Dec 12, 2015

Staff Emeritus
It doesn't, because there is nothing to radiate. You get radiation if you have a time varying multipole moment, and a constant current does not have that. Classically, each current element has a corresponding current element that exactly cancels its radiation. With discrete charges, this cancellation is not exact, but with 10^23 electrons, it's pretty darn close.

9. Dec 13, 2015

### sophiecentaur

OK so it's just a loop antenna carrying DC. It would only radiate the noise / random component of the current. OTOH, a single electron or a bunch would radiate energy.

10. Dec 13, 2015

### manzana

On a related note, the impedance of nothing(free space) turns out to be about 377 ohms! I always thought that was amazing. I guess it got decided in the Big Bang and has served us well. Kind of like PI...

11. Dec 13, 2015

### ehild

You speak about the wave impedance of free space. https://en.wikipedia.org/wiki/Impedance_of_free_space.
It has nothing to do with the resistance of a resistor. The dimension is resistance, but it is defined as the ratio of |E|/|H|, the amplitudes of the electric field and magnetic field in a plane wave travelling in free space.

12. Dec 13, 2015

Staff Emeritus
The impedance of free space is simply the speed of light, expressed in appropriate units, with some 4pi's tossed in.

13. Dec 13, 2015

### sophiecentaur

It has more implications than you suggest. An antenna is a matching device for transforming the free space impedance (which is resistive because there is no energy stored and it's all being 'lost' in space. The input impedance of an antenna will have a resistive component which accounts for the radiated power - just as if there were a metal film resistor, terminating the feed line. (ignore the reactive components if the antenna) Resistance is power dissipation - in any circumstances.

Last edited: Dec 13, 2015
14. Dec 13, 2015