## Power of Attraction

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.

## 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 (6.022×1023 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 4.836×1022 freely moving electrons (charge carriers) and an equal number of atoms (holes).

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 Arizona. 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 1.602×10-19 Coulombs, the total charge removed from the nickel equals:

Charge removed = (4.836×1022 electrons)×(1.602×10-19 Coulombs/electron) = 7.747×103 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/(4πε0r2) = 5.394×1011 Newtons

Where:

• q1 is the positive charge remaining on the nickel,
• q2 is the opposite charge placed on the battleship,
• ε0 is the electric permittivity of free space (8.854×10-12 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:

Lift = 5.394×1011 Newtons / (9.8 m/s2) = 5.504×1010 kg = 6.062×107 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 Arizona weighed 31,400 tones when fully loaded.

The nickel has the ability to lift not just 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 7×1015 volts. The energy required to accomplish the charging is: 1/2(CV2)=2.45×1019 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

### Reference

 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.

 Thanks to Thomaz Bryant for noticing that the email version of this ariticle incorrectly refers to the battleship Missouri as a sunken ship. The Missouri floats today alonside a tourist dock at Pearl Harbor. It is the USS Arizona that rests in a watery grave at the bottom of the harbor.