# Velocity of electrons and protons when current is induced through a loop of plasma

#### skullcracker

Is there an equation to find out the velocity of electrons and protons in a loop of plasma when a current is induced through it?Is the velocity just equal in magnitude and opposite in direction or is it opposite in direction and the velocity dependent on mass of the particles?(implying that an equal amount of force is exerted on the electrons and protons)

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#### sophiecentaur

Science Advisor
Gold Member
Re: velocity of electrons and protons when current is induced through a loop of plasm

Conservation of momentum would tell you that the relative magnitudes of velocities would be around 1:1800ma, where ma is the 'atomic' mass of the ions. (Big ions slow, small electrons fast)
Your suggestion would only apply to a Hydrogen plasma so you need to consider the total mass of the ions. I have assumed singly ionised particles, of course.

#### skullcracker

Re: velocity of electrons and protons when current is induced through a loop of plasm

So if I had a plasma which is a mixture consisting of an equal amount of protium and deutrium would the ratio of the velocities of electron, protium and deutrium (respectively)be 3600:2:1 ?

#### sophiecentaur

Science Advisor
Gold Member
Re: velocity of electrons and protons when current is induced through a loop of plasm

I think we need to think again about this.
Your numbers agree with momentum conservation so you may be right but I wondered whether they would hold for a mixture. Then, as I wrote the following, I came to a bit of an impasse. Here is my general thinking - I think it's worth sharing this sort of thing:

A protium plasma would have the ratio 1800:1 and a Deuterium plasma would have the ratio 3600:1 but could you be sure that the ion velocities would be 2:1 in ratio in a mixture? I should have thought that the KE of the ions would be the same so their velocities would be in the ratio 1:√2. But then the electrons would also have different velocities due to momentum conservation. This is a paradox.

I think my initial glib statement about momentum consideration could be at fault. This is not an isolated system and momentum can be transferred to the equipment / rest of the world so momentum of ions and electrons need not add up to zero. It would probably be better to assume that the work done on all the charges is the same. It would certainly be the case if the plasma were subject to an electric field across a gap - the eV would be the same for all. So I think, from energy considedrations, the ratios of velocity would be √(1800):1:1/√2 and to hell with momentum conservation.

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