A Figure in Griffith's Intro to Electrodynamics

[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.

 

[jtbell]

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."

 

[UltrafastPED]

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.

 

[DocZaius]

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.

 

[TSny]

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.