# Link between SR and a magnetic field

• arydberg
Van de Graff generator. There are no charges on the belt, so there is no current flowing. What happens when the moving charges are not on a wire? It's possible to generate a magnetic field from the moving charges without having them on a wire. An example is the belt in a Van de Graff generator.

#### arydberg

The seems to be a link between SR and a magnetic field Feynman mentions it in his "Lectures in Physics". The problem is the explanation is not finished. Feynman's assumes electrons travel at relativistic speeds while they are known to travel at very slow speeds.

It seems to me we need a better explanation.

Al

Purcell states you have tens of thousands of coulombs in conduction electrons in a 1 meter wire. I don't get it.

I get 1,600 coulombs in a 1 mm copper wire 1 meter long vol = .785 cm^3 mass = 7 grams or .0157 moles or 10 ^22 electrons or 1,600 coulombs.

Al

What difference does it make? Maybe he assumed a thicker wire or more conduction electrons. It doesn't change the algebra or geometry.

It just does not seem complete. To many assumptions. I assume the velocity of conductions electrons is a velocity distribution. I think there is more to be done here. The idea itself is very interesting but maybe it can be taken further.

Seems like a pretty vague objection, but by all means examine it more if you think it will be helpful.

Why would you look at individual electron velocities and not the flow of current itself?

Ask Purecll. Thats my point. I presume electricity is the flow of both negative as well as positive charges.

arydberg said:
Purcell states you have tens of thousands of coulombs in conduction electrons in a 1 meter wire.

Schroeder stated that in the referenced writeup of his talk. I don't have Purcell's book, so I don't know if he stated that.

arydberg said:
Ask Purecll. Thats my point. I presume electricity is the flow of both negative as well as positive charges.

Electricity in a wire is the motion of charge particles as a current/flow. Not as individual particles ... the individual electrons move extremely slow within a wire (I think this statement and the arguments are done/given in Griffiths).
What is changed by SR is the current...

arydberg said:
7 grams or .0157 moles

I get (7 g)/(63.5 g/mole) = 0.11 mole. That many electrons does have a total charge of about 10000 C.

arydberg said:
Ask Purecll. Thats my point. I presume electricity is the flow of both negative as well as positive charges.
The key question is: Does it make a difference?

You are mentioning several things here: the precise number of charge carriers, whether the charge carriers have a uniform velocity or a distribution, whether the charge carriers are positive or negative. You should work each of those out to see if they matter.

I never worried about your first or second concern, but the third one bothered me too. It only takes a few minutes to work it out, so it is a good exercise.

jtbell said:
I get (7 g)/(63.5 g/mole) = 0.11 mole. That many electrons does have a total charge of about 10000 C.
Yep, Thanks the number is 10,000 coulombs. not yet "tens of thousands of coulombs" but closer. My mistake.

What happens when the moving charges are not on a wire. An example is the belt in Van de Graff generator. Charges of one sign only are sprayed on the belt and then moved to the inside of the sphere. Is there a magnetic field from these moving charges. Has it been observed?

The magnetic fields of currents through non metallic conductors have certainly been measured. I don't know specifically about the current on a van De Graff generator, but we have certainly measured the magnetic field of currents through electrolytes and vacuum.

Given the Schroeder write up I would assume that there is no magnetic field due to the motion of a Van de Graff generator belt as there are no positive charges to balance out the negative ones sprayed on the belt. (Assuming of courses the charges carried by the belt are negative)

Why would they need to be balanced? Again, you should work this out yourself and see.

Consider a belt with a charge density ##\rho## moving at a velocity ##v<<c##. Consider two test charges at distance ##d## from the belt, one at rest and one moving alongside the belt at velocity ##v##. What is the force on the static charge? Use length contraction to determine the force on the moving charge in the belt's frame. Compare the two.

In the Schroeder treatment when you do the length contraction the negative charge density becomes different from the positive charge density yielding a net charge. With no positive charges what is the effect of the length contraction?