Understanding Electric and Magnetic Fields

[James98765]

I am a self taught physics enthusiast with a frustrating conceptual problem; I have been unable to come up with a reasonable visual model connecting electric and magnetic fields.

I first began visualizing electric fields as a spherical wave that expands into 3D space. This made since because of Coulomb’s inverse square law. When studying magnetism, I visualized field lines circling moving charges as described by Faraday. Here are my problems with the visual models:

How does a moving source charge create a magnetic field in space that is perpendicular to its electric field?
Why do charges moving through this magnetic field experience a force perpendicular to its velocity and the field?

I understand these might not be easy questions to answer in words. Am I asking these questions too early in my studies? I have already finished reading about Maxwell’s equations and electromagnetic waves but didn’t get the explanation I was hoping for. If a simple explanation doesn’t exist, can somebody point me in the right direction? Do I need a more focused textbook perhaps?

 

[jtbell]

I have already finished reading about Maxwell’s equations and electromagnetic waves but didn’t get the explanation I was hoping for.

Then (assuming you understand how Maxwell's equations work) you probably won't find the explanation you are hoping for. Maxwell's equations are as deep as it gets, at least in the context of classical electrodynamics. I doubt that quantum electrodynamics would provide such an explanation either, because it is more abstract and the connection with classical electrodynamics is rather subtle. I could say, "it's all because the universe obeys a local U(1) gauge symmetry," but then that raises an obvious question, "why does the universe obey..."

 

[yungman]

I too am self study on electromagnetics, but I am on the electronic engineering side. I notice there are difference between EM books for physics and engineering. EM books for engineering has a big section on time harmonic waves and phasor representation of TEM that talk about EM wave propagate in medium. I am not comfortable to explain myself, here is a very good book that I use and it will explain a lot better:

https://www.amazon.com/dp/0201128195/?tag=pfamazon01-20

Read chapter 7 on EM wave, 8 on transmission lines. I have a lot of books on electro dynamics and electromagnetics including Griffiths, Hayt & Buck, Popovic, Ulaby, JD Jackson Schwarz and Kraus. I notice books for physics don't use phasor representation which I found to be easy to understand and useful. By far Cheng's book is the best on fields and waves.

As I said I study on my own, I concentrate more on the math side of it. I just spent a year studying PDE, part of D'Alembert and part of the Green's function. I found this really gives me insight on the EM waves. I study vector calculus over and over and like you, try to explain what is divergent theorem, curl, Laplace, Poisson in English. Also spent time studying coordinate systems. These together give me more insight on EM waves. I am planning to study Complex Analysis in the future to complete the math portion. That is just me.

For PDE, check out the book by Stanley J Farlow "Partial Differential Equation for Scientists and Engineers". It explain a lot of PDE in English well. I use PDE by Asmar suppliment with book by Strauss. Asmar is easy to understand but limited, Strauss is a good book for follow up and on introduction of Green's function.

 

[stevenb]

Why do charges moving through this magnetic field experience a force perpendicular to its velocity and the field?

There is some discussion on this over here.

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

There is a PDF attachment in one of my posts that describes how Coulomb force and length contraction from relativity combine to produce magnetic force. The reason why a perpendicular force is created is obvious from this viewpoint (consider the case of two parallel wires with current).

 

[zonde]

How does a moving source charge create a magnetic field in space that is perpendicular to its electric field?
Why do charges moving through this magnetic field experience a force perpendicular to its velocity and the field?

Magnetic field vector is pseudovector, that means that it is like rotation axis.
Magnetic field line is related to physical phenomena that is happening in plane perpendicular to magnetic field line. The same way as rotation happens in plane perpendicular to rotation axis.

 

[Driftwood1]

How does a moving source charge create a magnetic field in space that is perpendicular to its electric field?
Why do charges moving through this magnetic field experience a force perpendicular to its velocity and the field?

Your assuming that an electric field is exactly analagous to a magnetic field.

If you had a conducting cylindrical wire connected to a voltage source, the electric field is bound by the physical limits of the wire. That is the electric field runs along and within the wire itself.

The magnetic field that is formed around the wire is circular and propagates outwards towards infinity - becoming weaker and weaker - ie approaching zero magentic field strength.

Electric fields are bounded and finite, magnetic fields are not restricted to this condition or limit. Both require polarity though

Look at the magnetic field in a torroidal coil. In this situation the magetic field lines are bounded within the torroidal coil.

What is the magnetic field outside the torroidal itself?

 

[yungman]

I am a self taught physics enthusiast with a frustrating conceptual problem; I have been unable to come up with a reasonable visual model connecting electric and magnetic fields.

I first began visualizing electric fields as a spherical wave that expands into 3D space. This made since because of Coulomb’s inverse square law. When studying magnetism, I visualized field lines circling moving charges as described by Faraday. Here are my problems with the visual models:

How does a moving source charge create a magnetic field in space that is perpendicular to its electric field?
Why do charges moving through this magnetic field experience a force perpendicular to its velocity and the field?
I think you have to go into quantum machenics to understand that. My understanding is there is really no magnetic field, it is a force due to slight difference of velocity of electrons in wires. I don't think you get answer in electromagnetics study.
I understand these might not be easy questions to answer in words. Am I asking these questions too early in my studies? I have already finished reading about Maxwell’s equations and electromagnetic waves but didn’t get the explanation I was hoping for. If a simple explanation doesn’t exist, can somebody point me in the right direction? Do I need a more focused textbook perhaps?

I did not get too deep into this because I am more interested in the macro effect rather than trying to go deep into quantum machenics to explain where the magnetic field comes from, just take the words of Maxwell's, Bio-Savart and Ampere's law.

 

[James98765]

Thanks I appreciate the help! I have been given a lot to think about which will help me conceptually.