Electricity and Magnetism: What Causes B Fields from Moving Charges?

[cragar]

In classical physics when we have a current we have a B field. So let's say we have a charged wire and then we apply a voltage and then current starts to flow. What happened when the charge was stationary and then moving to cause this B field. When the charge is at rest it has an E field, but when it starts to move does its changing E field induce a B field?

 

[Rap]

The most satisfying explanation is to look at it from the viewpoint of special relativity. In special relativity, there is a "spacetime distance" between two events. People divide that spacetime distance into a space part and a time part, and people in different inertial frames get different results for what is the space difference, what is the time difference. In the same way, there is an energy-momentum vector for a particle. People in different frames come up with different results as to what is the momentum part, what is the energy part. In the same way, there is an electromagnetic field tensor, and people in different frames come up with different results as to what is the electric field part and what is the magnetic field part. In your example, when the charge is stationary, there is only an electric field. If someone is moving along the wire, they will say there is an electric field and a magnetic field. When you get the charge moving, you will say there is an electric field and a magnetic field. To a person moving along with the current, they will say that there is no magnetic field, only an electric field. You are both looking at the same electromagnetic field tensor, but you both separate it out into electric and magnetic parts differently.

 

[cragar]

thanks for your answer. suppose the wire had no net charge therefore no E field . How would we explain the B field when the electrons started to flow .

 

[stevenb]

thanks for your answer. suppose the wire had no net charge therefore no E field . How would we explain the B field when the electrons started to flow .

A simple way to think about this is to consider the Lorentz contraction for the moving electrons vs. the stationary protons fixed in the atoms. A detailed view of this can be found in the document given in post number 3 here.

https://www.physicsforums.com/showthread.php?t=439258

The issue of what an observer sees for electric and magnetic field in a neutral conductor is not as straightforward as most people assume. Once you realize that the very very small Lorentz contraction due to the exreeeeeemly tiny drift velocity is enough to create magnetic effects, you are forced to think about what the fields are when you walk past a conductor with current flow in it. Consider that you can walk ten thousand times faster than the drift velocity of the charges ! Sit down and work out the math for this and it is quite revealing.

 

[Rap]

A simple way to think about this is to consider the Lorentz contraction for the moving electrons vs. the stationary protons fixed in the atoms. A detailed view of this can be found in the document given in post number 3 here.

https://www.physicsforums.com/showthread.php?t=439258

The issue of what an observer sees for electric and magnetic field in a neutral conductor is not as straightforward as most people assume. Once you realize that the very very small Lorentz contraction due to the exreeeeeemly tiny drift velocity is enough to create magnetic effects, you are forced to think about what the fields are when you walk past a conductor with current flow in it. Consider that you can walk a million times faster than the drift velocity of the charges ! Sit down and work out the math for this and it is quite revealing.

Yes, that's right. In a wire, the negatively charged electrons are moving, and the positively charged heavy metal ions are stationary. If you were to move along the wire at the speed of the electrons, you might say that now the positive ions were moving in the opposite direction, giving the same current, but no E field. But that would be wrong. Suppose the distance between the electrons and the ions were the same when you were stationary with respect to the wire. Then their densities are the same, and there is no E field, only a B field. But if you move along with the electrons, the distance between them becomes larger, because the distance was Lorentz-contracted when you saw them moving. That means the electron density goes down. The distance between the ions will decrease, because now they are Lorentz contracted. The ion density goes up. So, moving along with the electrons, you will see a net positive charge on the wire which gives an electric field, along with an increased B field due to the increased positive ion current.

PS - could somebody check this argument - it seems strange to me that in the second case there is both an electric field and an increased B field, but maybe its true.

 

[cragar]

thanks for your responses .