[hsdd] High-Speed Digital Design Newsletter - - Power of Attraction
- From: "Howard Johnson" <howie03@xxxxxxxxxx>
- To: <hsdd@xxxxxxxxxxxxx>
- Date: Mon, 14 Feb 2011 08:38:57 -0800
www.sigcon.com <http://www.sigcon.com/>
Power of Attraction
High-Speed Digital Design Online Newsletter: Vol. 14 Issue 01
Fully-formatted web version of this article:
www.sigcon.com/Pubs/news/14_01.htm
_____
If I'd put a nickel in my pocket every time I let a good idea pass by
without acting on it, I would be a rich man.
I would also have very saggy pants, some difficulty in walking, and, should
the mass of all those nickels aggregate to too great a sum, gaping holes
torn through the bottoms of my pants pockets.
This example illustrates a time-honored principle of engineering: that a
sufficiently large number of tiny forces cumulates to a powerful extreme.
A similar principle applies to the field of education. An educated person
accumulates a large number of small facts, the aggregate power of which
bestows upon the owner some measure of control over his or her destiny. The
power of knowledge is the "fifth force" in the physical universe, capable of
acting over great distances with significant influence.
In the field of electrical engineering, I help people build their store of
knowledge about high-speed digital system behavior, circuit layout, signal
propagation, noise, and grounding through my seminars, books, and films.
I'll be in the San Jose area May 2-10 and hope to see you at one of my
classes.
Today's article is not about the mass of a nickel, but rather the cumulative
effect of its electric charges.
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Power of Attraction
By Dr. Howard Johnson
In 2010, the United States mint produced 490,560,000 five-cent coins,
popularly called "nickels." Each nickel weighs 5 grams, comprising a mixture
of Copper and Nickel alloyed together in a ratio of 75% to 25% by weight.
The specific alloy mixture, size, and weight of this coin have been the same
since 1938.
Four-hundred ninety million is a mighty big number, but it looks puny in
comparison to the number of atoms in each nickel. If you remember a bit of
high-school chemistry, the number of atoms is ascertained by first dividing
the weight (5 grams) by the effective atomic weight of the alloy (62 grams
per mole) to determine the number of moles of material present. Multiply
that result by Avogadro's number (6.022x10E+23 atoms/mole) to find the
number of atoms.
Assuming that each atom in the 75/25 alloy contributes one free electron
from its outer 4s shell to the conduction band, the whole nickel coin
contains a total of 4.836x10E+22 freely moving electrons (charge carriers)
and an equal number of atoms (holes)[1].
Now imagine a nickel floating in air, supported on angel's wings. Position
the nickel 1 km above the surface of the Pacific ocean, directly above the
battleship Missouri.[2] On the count of three, magically remove all the
conduction-band electrons from the nickel and place them on the battleship.
The positively charged atoms remaining in the nickel will surely attract the
negatively charged atoms in the battleship. The question is, whether the
attraction will be enough to lift the weight of the ship from its watery
resting place at the bottom of Pearl Harbor.
Did I say, "Weight of the ship?" If you think of electrons as tiny, almost
massless particles that carry a minute electric charge, it may be difficult
to comprehend the magnitude of the forces involved.
Fortunately, rather than guessing based on intuition, we may calculate the
force mathematically from Coulomb's Law. We'll do the calculation in a
moment.
First, just contemplate the sheer amount of electric charge involved. Each
electron having a charge of 1.602x10E-19 Coulombs, the total charge removed
from the nickel equals:
Charge removed = (4.836x10E+22 electrons)x(1.602x10E-19 Coulombs/electron) =
7.747x10E+3 Coulombs
Removing electrons from the nickel at a rate of 1 amp, it would take more
than two hours to drain the nickel. That's a substantial amount of total
charge. In the world of batteries, we would rate that as 2000mAh. Is that
enough to lift a battleship? Well, perhaps not if you are talking about a
3.7V Li-Ion battery, but in this case it's not immediately clear what
voltage we are talking about, so hold off on your conclusion for a moment
while we do the force calculation.
F = q1q2/(4(pi)e0r2) = 5.394x10E+11 Newtons
Where:
* q1 is the positive charge remaining on the nickel,
* q2 is the opposite charge placed on the battleship,
* e0 is the electric permittivity of free space (8.854x10E-12
C2/N-m2), and
* r is the distance (1000 m) between the nickel and the ship.
Convert the force in Newtons into tons of lifting power in a gravitational
field of 1g:
Lifting power = 5.394x10E+11 Newtons / (9.8 m/s2) = 5.504x10E+10 kg =
6.062x10E+7 tons
I rendered the result in tons, because that's the unit of weight used for
battleships. The lifting power of the nickel, stripped of all its
conduction-band electrons, at a distance of 1 km, appears to be 60 million
tons. The battleship Missouri weighs 58,000 tones when fully loaded.
The nickel has the ability to lift not one, but a thousand battleships. Does
that number surprise you? Check the calculations yourself. In nature we
rarely observe electrons separated far from their host atoms precisely
because the electrostatic force is so incredibly strong.
What voltage is involved? You can estimate that from knowledge of the
capacitance of the nickel and the amount of charge placed on it. The nickel,
approximated as a conductive sphere with a diameter of 21 mm placed at a
height of 1 km, has a capacitance to Earth of about 1 pF. Charging that
capacitance to a level of 7000 Coulombs requires a voltage (V=q/C) of
7x10E+15 volts. The energy required to accomplish the charging is:
1/2(CV2)=2.45x10E+19 watt-seconds, or 6.8 million Gigawatt-hours-somewhat
more than the energy stored in a typical Li-Ion battery, wouldn't you say?
Obviously, such voltages and energies are impossibly huge, a fact that
highlights the exquisitely fine balance of negatively and positively charged
particles that exist in any practical circuit.
When we say a capacitor is "filled" with charge, it contains only a
miniscule excess of electrons on one plate, and a matching deficit on the
other. When we say current "fills" a conductor, an observer placed within
the body of the conductor, surrounded by a vibrant sea of zipping, bouncing
particles, would have a difficult time determining in which direction the
current flows. When Kirchoff says, "the sum of currents into a node equals
zero", he means that the electric force is so powerful that it is nearly
impossible to impose additional electrons, unwanted, into a circuit, or to
remove them.
The key point to remember from this article is that one can hardly change
the total number of electrons present within a circuit. Every electron that
exits the circuit must be accompanied by another moving in. That is the
principle underlying the concept of "signal current" and "returning signal
current."
Best Regards,
Dr. Howard Johnson
-------------------------------------------------------
References
[1] An atom of nickel in its natural state has two 4s electrons, but it may
not contribute both to free conduction in this alloy. Each atom of copper
contributes one electron. Since Ni is the minority constituent in the alloy,
that fine detail makes little practical difference to the thrust of the
article.
[2] <http://www.ussmissouri.com/> http://www.ussmissouri.com/
_____
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Howard Johnson conducts technical workshops for digital engineers at Oxford
University and other sites worldwide.
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