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Motivation to study electromagnetics?

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Old   February 2, 2019, 19:18
Default Motivation to study electromagnetics?
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Navarun Jagatpal
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I'm a graduate student, working on a PhD-ECE. I'm very interested in photonics, especially building practical real-world photonic devices. However, at my university, grad students have to study photonics and electromagnetics together. Therefore, I had to take a course last semester called Advanced Engineering Electromagnetics. The course used a textbook of the same name, written by Constantine Balanis, and I suspect that some people on this forum might be familiar with this book.

I didn't do well in the course. This was partly because I was extremely unmotivated. However, I do have to learn the concepts in the course, because I'm taking the qualifying exam in June. I'm hoping that people on this forum can help me with motivation.

My main question is, why should I care? I signed up for a degree in engineering. But then, this class didn't feel like an engineering class at all. It felt like it was just a lot of math and theoretical physics.

To me, engineering means building things. It means that a person asks me "Hey, can you to build a device that does XYZ?" And then I plan it out, I design the device, possibly using mathematical models as part of the design process. And then I buy the parts, and put them together, and I build the device. And then I give the device to the other person, and they can use it.

But it seems like this class and this textbook don't contain anything like that. They consist entirely of theory and theoretical problems. My professor himself described them as "toy problems." Why should I care about toy problems?

I want to ask everyone in this forum specifically about magnetic vector potential. It's something that came up repeatedly throughout the course, but I still don't understand why it's so important. First of all, what is it? Obviously it's a vector field, but what is it, physically? I've seen that it's defined by the equation:

\vec{B} =  \nabla \times \vec{A}

But, so what? That equation doesn't really tell me what it is, or why I should care about it. Can you touch it? Can you see it? Can you measure it? I know that \vec{B} can be measured, using a Hall Effect Sensor. But it seems that there is no way to measure \vec{A}.

Second of all, can you actually use \vec{A} to help build and design a device? It would be nice if someone could give me a specific real-world example, in which a customer says to an engineer "I want you to build a device that does XYZ." And then the engineer designs the device, and, as part of the design process, he writes down equations containing magnetic vector potential, and then he uses those equations to help him optimize and improve the device. Can anyone give me an example like that? (I guess the device would be an antenna, in this case? I honestly don't know. I'm completely lost here.)

This post really just scratches the surface of things that I didn't like about this course/textbook. There are many many other reasons why I was unmotivated, and frustrated, and confused, and I might start new threads in the future with my additional questions about this.
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Old   March 9, 2019, 09:00
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I don't think i can help you out regarding your frustration. You seem to be a very practially oriented person. Understanding electromagnetics requires quite some theory which you may have to fight with.

Regarding the vector potential, it is useful because magnetic fields are formed as rotational fields around electrical and displacement currents. This means they will have a somewhat complex physical shape that may be difficulto to understand/investigate when it comes to real world geometries. If you use the vector potential you will see a field distribution which might be easiert to relate to the current distribution.

Apart from that, the magnetic vector potential is often used to solve magnetic field distributions, be it in analytical form or with numerical methods.

Regarding the physical meaning, I think there are some experiments in quantum mechanics that imply that the magnetic vector potential can be viewed as the true underlying phenomenon rather than the magnetic field but I don't remember this so clearly. I don't know of any more common cases which cannot principially be explained with the B-field as well. But you will have a harder time in some cases
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Old   November 19, 2019, 05:34
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The magnetic vector potential is focused on because it's generally interesting to Physicists, and does have implications which are probably less interesting to Engineers. It's used primarily to make the maths easier from a practical perspective, because the Gauge invariance of the quantity means you can make it easier to deal with things.

Physicists use in relativity the four-potential A^\mu = (\phi, A) because an electromagnetic field tensor can be written as:

F^{\mu\nu} = \partial^\mu A^\nu - \partial^\nu A^\mu

There *are* also effects that can determine the magnetic vector potential. One of these is the quantum mechanical phenomena known as the Aharanov-Bohm effect. A particle travelling through a region where $\mathbm{B} = 0$ picks up a phase due to the magnetic vector potential.
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