# Self-Studying Electrodynamics- Am I doing it correctly?

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In summary: Two infinitely long conducting cylinders have their central axes parallel and separated by a distance ##c##. The radius of one is ##a## and the radius of the other is ##b##. If ##c >>a## and ##c>>b##, find an approximate expression for the capacitance of a length ##L## of this system.
So I am self-studying electrodynamics using Wangsness' Electromagnetic Fields textbook. Now, I have completed till chapter 21 (Maxwell's Equations). From the electrostatics part, out of the total end chapter problems for each chapter, I was able to solve all excluding 2 or 3. That is, if there were 20 end chapter problems for a certain chapter, I could solve 17-18. Is this performance good enough?

But for magnetism part, my performance has worsened. Out of say 20 end chapter problems, I could solve 15-16. Is this performance normal or do I need to put in more effort for magnetism?

So I am self-studying electrodynamics using Wangsness' Electromagnetic Fields textbook. Now, I have completed till chapter 21 (Maxwell's Equations). From the electrostatics part, out of the total end chapter problems for each chapter, I was able to solve all excluding 2 or 3. That is, if there were 20 end chapter problems for a certain chapter, I could solve 17-18. Is this performance good enough?

But for magnetism part, my performance has worsened. Out of say 20 end chapter problems, I could solve 15-16. Is this performance normal or do I need to put in more effort for magnetism?

I did something similar in preparation for my undergraduate studies. It sounds like you are doing well. Different people find different topics difficult, this is where an academic tutor would come into help. The question of "good enough" is a little ambiguous , good enough for what?

BvU

By "good enough" I was trying to compare myself to an average student self-studying electrodynamics. How does my performance fare when compared to the performance of such a student?

By "good enough" I was trying to compare myself to an average student self-studying electrodynamics. How does my performance fare when compared to the performance of such a student?
I suggest that the average student would struggle greatly to learn EM through self study.

You could take a look at some of the problems in the homework forum on here. You could post a problem from your textbook that you couldn't do.

It's difficult to know without seeing your work and your approach to problems just how competent you are at a subject.

Most of the problems from a chapter in electrostatics that I could not solve were the last one or two problems from that chapter. Two of the problems:

1. An infinitely long cylinder has its axis coinciding with the ##z##-axis. It has a circular cross section of radius ##a## and contains a charge of constant volume density ##\rho_{ch}##. Find ##\vec{E}## at all points, both inside and outside the cylinder. Hints: use cylindrical coordinates for integration; for convenience, choose the field point on the x-axis (Will this be general enough); you will probably need this definite integral $$\int_0^{\pi} \frac{\left( A - B cos(t) \right)}{A^2 - 2 A B cos(t) + B^2} \, dt = \frac{\pi}{A} \mathrm{if} A^2 > B^2 and = 0 \mathrm{if} A^2 < B^2$$

2. Two infinitely long conducting cylinders have their central axes parallel and separated by a distance ##c##. The radius of one is ##a## and the radius of the other is ##b##. If ##c >>a## and ##c>>b##, find an approximate expression for the capacitance of a length ##L## of this system.

Now for magnetism part, problems I could not solve included:

1. An infinitely long straight wire carrying a constant current ##I## coincides with the ##z##-axis. A circular loop of radius ##a## lies in the ##xz##-plane with its center on the positive ##x## axis at a distance ##b## from the origin. Find the flux through the loop. If the loop is now moved with constant speed ##v## parallel to the ##x##-axis and away from ##I##, find the emf induced in it. What is the direction of the induced current
(I could not find the flux in the above question)

2. An electromagnetic "eddy current" brake consists of a disc of conductivity ##\sigma## and thickness ##d## rotating about an axis passing through its center and normal to the surface of the disc. A uniform ##\vec{B}## is applied perpendicular to the plane of the disc over a small area $a^2$ located a distance ##\rho## from the axis. Show that the torque tending to slow down the disc at the instant its angular speed is ##\omega## is given approximately by ##\sigma \omega B^2 \rho^{2} a^2 d##

What else do I need to post so that my preparation can be evaluated?

Most of the problems from a chapter in electrostatics that I could not solve were the last one or two problems from that chapter. Two of the problems:

1. An infinitely long cylinder has its axis coinciding with the ##z##-axis. It has a circular cross section of radius ##a## and contains a charge of constant volume density ##\rho_{ch}##. Find ##\vec{E}## at all points, both inside and outside the cylinder. Hints: use cylindrical coordinates for integration; for convenience, choose the field point on the x-axis (Will this be general enough); you will probably need this definite integral $$\int_0^{\pi} \frac{\left( A - B cos(t) \right)}{A^2 - 2 A B cos(t) + B^2} \, dt = \frac{\pi}{A} \mathrm{if} A^2 > B^2 and = 0 \mathrm{if} A^2 < B^2$$

2. Two infinitely long conducting cylinders have their central axes parallel and separated by a distance ##c##. The radius of one is ##a## and the radius of the other is ##b##. If ##c >>a## and ##c>>b##, find an approximate expression for the capacitance of a length ##L## of this system.

Now for magnetism part, problems I could not solve included:

1. An infinitely long straight wire carrying a constant current ##I## coincides with the ##z##-axis. A circular loop of radius ##a## lies in the ##xz##-plane with its center on the positive ##x## axis at a distance ##b## from the origin. Find the flux through the loop. If the loop is now moved with constant speed ##v## parallel to the ##x##-axis and away from ##I##, find the emf induced in it. What is the direction of the induced current
(I could not find the flux in the above question)

2. An electromagnetic "eddy current" brake consists of a disc of conductivity ##\sigma## and thickness ##d## rotating about an axis passing through its center and normal to the surface of the disc. A uniform ##\vec{B}## is applied perpendicular to the plane of the disc over a small area $a^2$ located a distance ##\rho## from the axis. Show that the torque tending to slow down the disc at the instant its angular speed is ##\omega## is given approximately by ##\sigma \omega B^2 \rho^{2} a^2 d##

What else do I need to post so that my preparation can be evaluated?

Problem 1 would appear to be a simple application of Gauss's law. I'm not sure why you would, as suggested, integrate from first principles.

I assume you know Gauss's law?

Using the result of problem 1 should help with problem 2. This is a bit trickier.

In general I would say these are problems that only test your basic knowledge of electrostatics.

You ought to post these in the homework section.

Yes I was able to solve the first problem using Gauss' law. The reason I added this problem to the list above was that the question expects me to solve it using first principles which I couldn't.

I'll post the remaining questions in the homework section

## 1. How do I know if I am understanding the concepts correctly?

The best way to gauge your understanding is to test yourself regularly. Try solving practice problems or explaining the concepts to someone else. If you can do so confidently and accurately, then you are likely understanding the material correctly.

## 2. Is it necessary to have a strong mathematical background to self-study electrodynamics?

While a strong mathematical background can certainly be helpful, it is not necessarily a requirement for self-studying electrodynamics. It is important to have a basic understanding of calculus and vector algebra, but you can also learn these concepts as you go along.

## 3. How can I stay motivated while self-studying electrodynamics?

One way to stay motivated is to set small, achievable goals for yourself. This can help you track your progress and feel a sense of accomplishment. It can also be helpful to join a study group or find a study partner to keep you accountable and motivated.

## 4. How much time should I dedicate to self-studying electrodynamics?

The amount of time you should dedicate to self-studying electrodynamics will vary depending on your goals and learning style. However, it is recommended to spend at least 1-2 hours per day consistently studying and reviewing the material.

## 5. Are there any online resources that can help with self-studying electrodynamics?

Yes, there are many online resources available to help with self-studying electrodynamics. Some popular options include online lectures, practice problems, and interactive simulations. You can also join online forums or discussion groups to connect with other students and ask questions.

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