Help with Jackson Electrodynamics Notation

In summary, the conversation discusses difficulties with Jackson's notation in relation to Green's theorem. The main issue is understanding the physical relevance of the prime in the notation, particularly in regards to the location of the point charge in "Green Space". The conversation also touches on problem 2.7, where the unprimed coordinates represent the location where the potential is being found, and the primed coordinates represent the location of the charge on the disk. The conversation ends with a question about Jackson's interpretation of the delta function in equation 1.36.
  • #1
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Homework Statement



I am having some difficulty with Jackson's notation.

I am coming from an engineering (not physics) background.

First of all, on Page 36 at the bottom of the page, Jackson uses the Dirac delta function d(x-x'). When he integrates his answer is the function at x instead of at x' as I would expect from the discussion on Page 26. Maybe this doesn't matter, but remember, you are talking to an engineer, so I need to understand the physical relevance.

My real question is, when Jackson starts working with Green's theorem, he uses x' as the location of his point charge in "Green Space" and as his integration variable. He then makes is integrals over d3x' and da'. Then he takes n' to be his normal vector and changes it to z' (n'=-z'). I understand why n=-z, but I don't understand the physical significance of the prime in this case. I still think that the prime refers to the location of the point charge in "Green Space".

Homework Equations



See Above

The Attempt at a Solution



This is in reference to problem 2.7 which I am working, but I am not asking for a solution. Just need help with the concept.

Thanks in advance
 
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  • #2
OK so I wrestled with Jackson Problem 2.7c some more and I think I have come to the following realization (is this right?):

The unprimed coordinates (r,th,z) are the location where we are trying to find the potential (our viewpoint). The primed coordinates (r',th',z') are the location of the charge on the disk (which is why we integrate in the primed coordinates because we are integrating to find the charge distribution). So in Problem 2.7c where we have to find the potential along the z axis, we set unprimed r=0 and integrate WRT r' (and th') over the surface of the disk. At least that gives me the correct answer.

Is that correct?

Also, I still don't understand why Jackson P 36 (blue version) seems to interpret the delta function "backwards" in eq 1.36. Can anyone help me with that?
 

1. What is the Jackson Electrodynamics notation?

The Jackson Electrodynamics notation is a mathematical notation used to represent electromagnetic equations in physics. It was introduced by physicist John David Jackson in his textbook "Classical Electrodynamics". It is commonly used in advanced courses and research in the field of electrodynamics.

2. Why is the Jackson Electrodynamics notation used?

The Jackson Electrodynamics notation is used because it is a concise and convenient way to represent complex electromagnetic equations. It uses vector and tensor notation, making it easier to express and manipulate equations involving electromagnetic fields and their interactions with matter.

3. What are some examples of the Jackson Electrodynamics notation?

Some examples of the Jackson Electrodynamics notation include the use of boldface letters to represent vectors, such as the electric field E and magnetic field B, and the use of subscript and superscript indices to represent components and operations, respectively. For example, in the equation ∇²E = -μ0J, ∇² represents the Laplacian operator, E represents the electric field, and J represents the current density.

4. How can I learn and become proficient in using the Jackson Electrodynamics notation?

To become proficient in using the Jackson Electrodynamics notation, it is important to have a solid understanding of vector and tensor operations, as well as the basic principles of electrodynamics. Practice and familiarity with the notation through solving problems and working through examples is also key. Additionally, consulting textbooks or online resources on the subject can also be helpful.

5. Are there any common mistakes to avoid when using the Jackson Electrodynamics notation?

One common mistake to avoid when using the Jackson Electrodynamics notation is mixing up the order of indices. This can lead to incorrect equations and solutions. It is also important to pay attention to the notation used for vector and tensor operations, such as multiplication and differentiation, to ensure accurate representation of equations. Additionally, it is important to double-check calculations and equations to avoid any errors or typos.

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