Understanding the behavior of E fields inside wires

[Jdo300]

Hello All,

I'm currently trudging through my physics class which is teaching about electric and magnetic fields, and their interactions. As I have been reading through the textbook, I have been trying to formulate ideas and understand exactly what is happening inside of current carrying wires. I have been trying to visualize what the E fields inside a copper wire do immediately after a voltage potential is applied, and immediately after the charges start to flow.

To make sure that I understand this right, let’s say we have a length of wire shorted across a battery that applies a potential difference of 1 volt from one end to the other. Assuming that I am interpreting this correctly, there will be an E field setup in the wire with the vector pointing from the negative side of the battery to the positive side; and because of Kerchhoff’s voltage law, we can calculate the amount of current that will flow based on I = V/R with R being the resistance of the wire (assuming we have an ideal battery for simplicity).

So, after the voltage potential is applied, it is the E field in the wire that pushes the charges through and creates the current right? This resulting current flow produces a magnetic field whose vector, B, is at right angles to the current flow vector (left hand rule for electrons). Ok, this is where I started asking questions.

I know that magnetic fields will exert a force on moving charges as they move perpendicular to the field. So in the case of the wire, immediately after the charges start to move and the magnetic field is created, do the charges not get forced towards the outside of the wire? So for an instant the wire has a radial E field with the negative end being the outside of the conductor and the positive side being the center? If my assumptions are true, I know, from reading about the Hall Effect, that the resulting E field eventually produces a force that is equal and opposite the force produced by the magnetic field which keeps the charges from moving radially outwards further. So, here are my questions:

1. Is what I described anywhere close to what is actually happening?

2. If I made the right assumptions, is there a way to predict how far the charges will move towards the outside of the wire before the E field cancels their movement if I know the B field strength, the amount of current, and the cross section of the wire?

3. Is there a way to determine how fast this effect takes place (how long it takes the electrons to move from their neutral state to the polarized state?

4. During the instant that the electrons rush towards the outside of the wire (if this really does happen), is there a radial magnetic field produced by the charges that emanates from the wire?

Ok, that’s all I have for now. I have more questions but I’ll wait to ask those since I am already going on a lot of assumptions here. Any help/ input/ corrections are greatly appreciated.

Thanks,
Jason O

 

[NoTime]

It's called the skin effect.
You should be able to find more info under that heading.

Generally it is a consideration for high frequency circuits.
However, the initial turn on counts as high frequency so it sounds like you have it about right.

 

[sir-pinski]

.

Hi Jason,

It's great that you're actively trying to understand the behavior of E fields inside wires. It can definitely be a complex topic, but with some visualizations and simplifications, it can become more manageable.

To answer your first question, yes, your understanding is generally correct. The E field inside a wire is created by the voltage potential applied by the battery, and it is this E field that pushes the charges through the wire, creating the current. And as you mentioned, the resulting current also creates a magnetic field around the wire.

In terms of your second question, predicting how far the charges will move towards the outside of the wire is a bit more complicated. It depends on factors such as the wire's resistance, the strength of the magnetic field, and the amount of current flowing. Additionally, the shape and material of the wire can also play a role. However, there are mathematical equations and simulations that can help determine this distance.

Your third question is also difficult to answer because it depends on the specific circumstances and materials involved. The movement of electrons in a wire is incredibly fast, on the order of nanoseconds. However, the polarization of the wire and the establishment of a steady-state current may take longer.

Regarding your fourth question, there may be a small radial magnetic field produced by the charges as they move towards the outside of the wire, but it would likely be very weak and quickly dissipate. The main focus is on the external magnetic field created by the current flowing through the wire.

I hope this helps clarify some of your questions. Keep up the curiosity and keep asking questions. That's the best way to understand and learn about complex topics like this. And don't hesitate to reach out for more help or clarification. Good luck with the rest of your physics class!