[Amps] Physics 101 - Charges, Electric Fields, and Currents

[Jim Garland]

I'd like to try and clear up a few misconceptions about charges and
currents. As most of you know, physicist J.C. Maxwell in 1861 published the
four equations bearing his name that described the properties of
electricity. He made no mistakes in his equations or any wrong assumptions
about the signs of charges. In fact, his equations never mentioned electrons
or protons, neither of which had yet been discovered. However, even if they
had been discovered, their discovery would not have changed his equations.

            The key idea in Maxwell's equations is the concept of electric
and magnetic fields. This was a huge breakthrough in human understanding.
Today, we know there are other kinds of fields - the gravitational field,
two kinds of nuclear fields, and other more arcane ones. Maxwell observed
that there is an electric field associated with every electric charge. An
electric field is an example of a vector field, which means that at all
points in space it has both a magnitude and a direction. For a point
positive charge, the electric field radiates outwards to infinity. For a
negative charge, like an electron, it points inward from infinity towards
the charge. 

            Now here is a key point, often not appreciated. While we think
of point charges like electrons as tiny little particles, in fact they are
huge. So huge in fact that each electron literally extends throughout the
observable universe (aside from a few subtleties). The reason is that the
electron's electric field is an integral part of the electron. If you wiggle
an electron, the entire electric field cloud around it also wiggles, with
the ripple spreading outward through the cloud at the speed of light.

            These fields are not just abstract, mathematical concepts. If
you hold a charged object in "empty" space, it will be pushed on by whatever
the value of the electric field is at that point in space. If the electric
field is too strong, and you get too close, it will kill you. Fields
permeate all of space. In space, matter is pretty scarce, but fields are
everywhere.

            Now consider a ball of matter that has a bunch of positive
charges on it and contemplate what happens if we make the ball less
positive. We can do this by stripping away some of those positive charges,
thus creating a "wind" of positive charges that flows away from the ball.
This wind of positive charges creates an outward flow of electric current,
but it is not the same thing as an electric current. The electric current is
a more abstract concept that takes into account both the direction the wind
is blowing and the sign of the charge carred in the wind. Like an electric
field, the electric current is also a vector field that has both a magnitude
and a direction at all points in space. In this example, the direction of
the electric current vector points away from the ball.

            Of course we can also make the ball less positive by adding
negative charges to it. Adding negative charges creates a wind of negative
charge that flows in toward the ball. However the resulting electric current
is still outward, because the minus sign on the negative charge cancels the
minus sign on the direction of the inward pointing wind. In other words, the
value of the current vector field is exactly the same, whether we have an
inflow of negative charges or an outflow of positive charges. And it's a
damn good thing it's the same, because if it wasn't all of ham radio, in
fact all of electronics could not exist.

            I know some of you are puzzled by the seeming paradox of all
this. To some, it seems odd and non-intuitive that heating a filament in a
vacuum tube to boil off electrons would cause current to flow from a distant
anode toward the filament. But there is no paradox. The paradox is really
just a failure to understand that electric current is a generalized concept,
in which a positive charge moving to the right is exactly equivalent to a
negative charge moving to the left. Electronics is filled with these kind of
seemingly non-intuitive things. For example, we often hang a filter
capacitor on a bridge rectifier to shunt the AC ripple current to ground.
Yet there is no charge that passes through the filter capacitor. The only
thing between the plates of the capacitor is an electric field.

            All of this was figured out about a hundred and fifty years ago
by some very bright people who devoted their lives to understanding it. I
think we owe them the benefit of the doubt. If we don't understand what they
did, then the problem lies with us, not them. If that's the case, then it
may be time for us to start hitting the books and try to be a bit more
flexible in our thinking.

 

73,

Jim Garland W8ZR