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Re: gauge invariance of funny capacitor.



At 07:06 AM 3/3/01 -0500, Ludwik Kowalski wrote:

infinity where V4, as usual, was assumed to be zero.
....... In other words, the infinity is a very large object on
which potential is zero. What is wrong with assigning zero
to infinity? Why did my teacher criticize this in his last
message under this thread?

It depends on context. By way of analogy, consider the following contrast:
a) you are free to go downtown tomorrow and participate in a
certain political rally.
b) you are required to go downtown tomorrow and participate in a
certain political rally.

Case (a) exemplifies freedom; case (b) exemplifies the opposite. If you
go to the rally, nobody knows what that means, unless they know the context.

Gauge invariance is a freedom. You are free to choose V4=0. But you are
equally free to choose some other value. And most importantly, you must
not assume that your choice is binding on anybody else.

There is physics in this. The charge distribution is
gauge-invariant. That means there is a many-to-one mapping from
potential-distributions to charge-distributions. A many-to-one mapping is
obviously not uniquely invertible.

It is in this context, namely the search for a unique inverse, that the
assumption that V4=0 was questioned and must be questioned.