# A Figure in Griffith's Intro to Electrodynamics

• DocZaius
In summary, the figure in question is meant to visually demonstrate the concept of self-inductance, showing how a changing current in a loop can induce an electromotive force in the loop itself. The "tiny loops" in the figure represent holes in an imaginary surface and serve to illustrate the magnetic field lines piercing the surface. The figure aligns with equation (7.25) which defines self-inductance, and no changes in current are necessary for this definition.
DocZaius
A Figure in Griffiths' Intro to Electrodynamics

I am really loving this book. But I have come across a figure whose purpose I just don't understand. It is shown when Griffiths is introducing the concept of self-inductance. He talks about how a changing current not only induces an electromotive force in other loops, but in itself as well. Then he refers the reader to the attached figure.

I have no idea what to make of the intended point for this figure. The phenomenon in question is due to a changing current. There is no hint of a change in time for the current in the figure. I am guessing he intends to make a point about these B fields going through these tiny loops inside the main loop? I simply don't get it. Anyone have an idea about the intended meaning of the figure in the context of self-inductance? (stressed to deter an answer that would consist of: "current in a loop generates a B field!")

Just to be clear, I understand the concept just fine, I am merely curious about the figure.

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That figure doesn't do much for me, either. He's apparently trying to make self-induction plausible. I would have drawn two identical loops, very close to each other at all points, like the two conductors in a loop of household "lamp cord", and then said something like: "Now, let the spacing between the conductors approach zero. The flux of B through them becomes equal. Any change in I in conductor #1 not only induces an emf in conductor #2, it must also induce the same emf in conductor #1 itself."

Griffith's is showing that the current in a single loop generates a B-field; he shows an arbitrary flux in diagram 7.32.

If there are two loops, then you have mutual inductance; he is describing self inductance.

UltrafastPED said:
Griffith's is showing that the current in a single loop generates a B-field; he shows an arbitrary flux in diagram 7.32.

That concept had been introduced a 100 pages prior in the book. If that's purely what he intends to show, it seems a little late.

If there are two loops, then you have mutual inductance; he is describing self inductance.

In the text he is. But in the figure? Inductance concerns changing currents and there is no indication of a current changing in time in the figure. Nor really is there an indication of how that is affecting the current itself.

Oh well, it could just be that there is no good answer and the figure is simply not helpful.

DocZaius said:
I am guessing he intends to make a point about these B fields going through these tiny loops inside the main loop?

Those "tiny loops" are just holes in an imaginary surface that subtends the current loop. I think they were meant by the artist to help visualize that there are magnetic field lines piercing the surface. See page 311 for a similar figure.

The current ##I## in the loop produces a magnetic flux ##\Phi## through the loop. The diagram goes with equation (7.25) that defines the self-inductance ##L##. There's no need to imagine the current changing for this definition.

## 1. What is "A Figure" in Griffith's Intro to Electrodynamics?

"A Figure" is a term frequently used in Griffith's Intro to Electrodynamics to refer to the diagram or illustration accompanying a particular concept or equation. These figures are meant to aid in understanding the material and provide visual representations of abstract concepts.

## 2. How can these figures be helpful in understanding electrodynamics?

The figures in Griffith's Intro to Electrodynamics can be helpful in understanding electrodynamics by providing a visual representation of the concepts being discussed. This can make the material easier to grasp and remember, as well as help readers develop a deeper understanding of the subject.

## 3. Are the figures in Griffith's Intro to Electrodynamics accurate representations of the concepts being discussed?

Yes, the figures in Griffith's Intro to Electrodynamics are carefully designed to accurately represent the concepts being discussed. They are created based on the author's extensive knowledge and understanding of electrodynamics, and are meant to provide a clear and accurate visual aid for readers.

## 4. Can the figures in Griffith's Intro to Electrodynamics be used for reference?

Yes, the figures in Griffith's Intro to Electrodynamics can be used for reference. They are often used by students and researchers as a quick visual reminder of a particular concept or equation. However, it is important to also refer to the accompanying text for a full understanding of the material.

## 5. Are there any supplemental materials available for the figures in Griffith's Intro to Electrodynamics?

Some supplemental materials, such as interactive simulations or animations, may be available for certain figures in Griffith's Intro to Electrodynamics. These can provide a more dynamic and engaging way to interact with the material and gain a deeper understanding of the concepts. However, the figures themselves are usually sufficient for understanding the subject matter.

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