magnetic fields and electron kinetic energy

[Neil9327]

15 years ago when I was a physics student I wondered whether for a coil with a dc current flowing through it the energy contained within the resultant magnetic field is equal to the kinetic energy of the electrons flowing around that coil.

Since then Ive worked in sales and computing, and have forgotton all my favourite theories that would have allowed me to calculate it.

 

Does anyone know the answer?

[Cloud]

Even I don't fully understand this. Yet I'll attempt.

 

For the energy in the magnetic field - this would be measured as energy density(in atmospheres/pressure).

 

I don't know if there is a connection to kinetic energy.

 

0.5 x (mass of electrons in coil) x (velocity of electrons in coil)^2 =

x no. of atmospheres

 

I mean - this energy density would have to be converted into joules (energy). That impossible.

[s pepperchin]

Are you asking if there is a relation between the potential energy of a particle in the magnetic field and the kinetic energy of the electrons flowing through the coil? If that is what you are saying then I am sure there is a way to figure out a relation between the current in the wire and the position and charge of the particle.

[Neil9327]

I was thinking of the scenario where you have a DC current running through a coil which is one side of a transformer. A static magnetic field runs round the ferrous core of the transformer, and if my memory serves me right this has a specific number of joules of energy associated with it. This energy can be seen when the DC current is shut off - the field causes a current to flow in the other side of the coil (assuming its ends are connected across a resistor) supplying voltage and current (this principle being used when AC current sends a continuous power across).

 

I'm remembering a little more now: A coil has an inductance L, and the energy carried in the field is half L i squared (where i is the current).

 

Hmmm I wonder whether I've answered my own question here. If i is constant then the kinetic energy of the electrons will be constant, but you can add materials into the coil to change the inductance without changing the coil itself.

[s pepperchin]

Hmmm I wonder whether I've answered my own question here. If i is constant then the kinetic energy of the electrons will be constant, but you can add materials into the coil to change the inductance without changing the coil itself.

 

How does this change in inductance change the kinetic energy of the electricity on the other coil, or the whole system for that matter?

[s pepperchin]

I checked one of my physics books and the equation for the Potential energy of an inductor is:

 

[math]U_L=\frac{1}{2}LI^2[/math]

 

and the equation for inductance is :

 

[math]L=\mu_0 A ln^2[/math]

 

when the inductor has a material in the coil the [math]\mu_0[/math] is replaced by

 

[math]\mu=\mu_0(1-\chi_m)[/math]

 

[math]\chi_m[/math] is the magnetic susceptibilty of the materieal

 

However an inductors kinetic energy would just be the relativistic kinetic energy of the electrons in the coil.

 

This is the equation for reletivistic energy.

 

[math]E=\frac{mc^2}{\sqrt{1-\frac{u^2}{c^2}}}[/math]

 

I haven't put these all together yet but I figured that since you were interested I would give you a few eqtns to work with while I also work on it and see what we get.

[swansont]

15 years ago when I was a physics student I wondered whether for a coil with a dc current flowing through it the energy contained within the resultant magnetic field is equal to the kinetic energy of the electrons flowing around that coil.

Since then Ive worked in sales and computing' date=' and have forgotton all my favourite theories that would have allowed me to calculate it.

 

Does anyone know the answer?[/quote']

 

It almost certainly isn't. The kinetic energy of electrons in a conductor is very small; the drift velocity is of order of millimeters per second, while in a vacuum, accelerating the elctrons through the same potential difference you would get a kinetic energy of KE= Vd. Yet, if the currents are equal, each beam would yield the same magnetic field.