Re: [Phys-l] transformer question

[John Denker <jsd@av8n.com>]

On 08/13/2009 09:04 PM, Bernard Cleyet wrote:

> I was brought up by Mr Harnwell who devotes ~ 13 densely written  
> pages to the subject, ........

That's good to know.  There is an amazing dearth of
references on the subject.


> bc thinks J. D. was brought up by Harnwell or similar author.

Me?  Absolutely not.

I was brought up by wizards who would never spend 13 
sentences on this subject, let alone 13 pages.

There is an important pedagogical point here:  They didn't
spoon-feed us anything.  They made a point of teaching
us the general idea, on the theory that if we ever needed
the details we could work out the details on our own.

I don't recall exactly, but I reckon there were one or two
physics homework problems that required finding the voltage
given the charge.  There might have been a couple sentences 
of instructions:  "Electromagnetism is linear.  Linearity 
implies superposition."  The homework didn't count for 
credit, so we never actually did the homework (unless it
looked challenging or interesting).  But we always _looked_ 
at the homework.  In this case we concluded yeah, linearity
implies superposition, and yeah, if we live to be 1000 
years old we will never forget this.  So we went on to 
looking at the next problem.

Then in engineering class somebody probably said we have 
several inputs and several outputs and a linear system.
It can be described by a __ __ __ __ __ __.  Fill in the 
blank.  It's a six letter word that starts with "M" and 
ends with "ATRIX".

Then they said this is called the capacitance matrix.  The
off-diagonal elements are the "mutual" capacitances while
the diagonal elements are the "self" capacitances.  

  I think they forgot to tell us that because of gauge 
  invariance there's really no such thing as a self 
  capacitance.  Or (more likely) I slept through that bit.  
  In any case, I had to figure that bit out on my own, 
  many years later.

I don't recall hearing or reading anything about non-ideal
transformers or mutual inductances ... but they *did* tell
us "the same equations have the same solutions" and if we
live to be 2000 we will never forget that.  And the equations
for inductors are almost the same as the equations for 
capacitors, given a trivial change of variables.

I got into finite element modeling so long ago I forget 
the first application.  I got into FEM applied to non-ideal
magnetic materials when helping my father design a solenoid 
valve for some NASA or Air Force rocket.

==============

The details of my story are not important.

The point I'm trying to make is this:  I am continually
amazed when people ask me who taught me this-or-that
subject or where I read about it.  The answer, 90% of 
the time, is that nobody taught me anything about that
subject.  They just taught me how to figure stuff out.

You know the proverb about giving somebody a fish versus
teaching them how to catch their own fish.

If you want to see some of the capacitance-related fish
I have caught, see
  http://www.av8n.com/physics/capacitance.htm
  http://www.av8n.com/physics/laplace.htm

... but to repeat the main point, I don't recommend you
memorize what it says there;  just understand it well
enough so that if/when a similar problem crops up you
will be able to derive whatever you need.