Popular Science

Quite recently, a close acquaintance of mine found themselves confronted with the rather perplexing quandary of why electric forces do not manifest themselves prominently on the scale of the human body. Perhaps it is enjoyable like most of the good physics problems, and for a new student of physics, at least, its message would be completely memorable.

The problem goes like this: What would happen if your body suddenly lost 1% of its electrons?

Now, 1% may not sound like a big deal. After all, there is almost no reason for excitement or concern when you lose 1% of your total mass. However, in the event that you experience a loss of 1% of your electrons without a corresponding loss of an equal number of protons within your bodily composition, a substantial quantity of positive electric charge remains unbalanced and unneutralized. Furthermore, it is imperative to acknowledge that nature, in all its complexity, cannot tolerate the notion of its most potent force being left unreciprocated.

For a human body of mass of about 80 kg contains something like 2×1028 protons, and an almost exactly equal number of electrons. Losing 1% of those electrons would mean that the body acquires an electric charge of 2×1026 electron charges or about 4×109 Coulombs. Now, 4 billion Coulombs may seem to be a silly amount of charge. But, for instance, it is about 300 million times more than what gets discharged by a lightning bolt. So, in some sense, losing 1% of your electrons would be like getting hit by 300 million lightning bolts at the same time.

Things get even more dramatic if you start to think about the forces involved. Again, I am wondering, what if these charges rushed into the body, those 4 billion Coulombs split in half and flowed to opposite extremities? Say, each hand suddenly acquired a charge of 2 billion Coulombs. The force between those two hands (spread apart, about 6 feet) would be 1027 Newton, which translates to about 1026 pounds. Needless to say, the body would not retain its structural integrity.

Of course, in addition to the forces pushing the extremities of this body apart, there would also be a force similar in magnitude pulling me toward the ground. You may recall that when an electric charge is next to a grounded surface (like, say, the ground), it induces some opposite charge on that surface in a way that acts like an “image charge” of the opposite sign. In this case, the earth would accumulate a huge amount of negative charge around the feet so as to create a force like that of an “image of body”. Because of my 4 billion Coulombs, the force between body and “image body” would be something like 1023 tons. To give that some perspective, consider that something with the same mass but, on the other hand, the planet Earth weighs only about 1021 tons. So, the force pulling me towards the Earth would be something like the force of a collision between the Earth and the planet Saturn.

But my hypercharged body would not only crush the earth. It would also break open the vacuum itself. At the instant of losing that 1% of electrons, the electric potential at the edge of the body would be about 40 exavolts. This is much larger than the voltage required to rip the vacuum apart and create electron-positron pairs. So my erstwhile body would be the locus of a vacuum instability, in which electrons would be sucked in while positrons would be blasted out. In short, if I lose 1% of my electrons, I would not be a person anymore. It would be a bomb. So imagine yourself as A Coulomb bomb, with an energy equivalent to that of ten trillion (modern) atomic bombs, which would surely destroy the planet. Hence, just by removing only 1 out of every 100 of your electrons.

The moral of this story, of course, is that nothing of observable size will ever get 1% charged. The Coulomb interaction cannot be thus toyed with. All of the chemistry and biology functions by the interactions between just a few charges at a time, and their effects are plenty strong as they are. As an explorer, I worked on all sorts of problems that involved the Coulomb interaction, and occasionally, my proposed solution would be very wrong. The worst kind of wrong was the one that made my advisor remark, “What you just created is a Coulomb bomb,” which meant that I had proposed something that wasn’t neutral on a large scale. It's one thing to feel like you just solved a problem incorrectly. It’s another to feel like your proposed solution would destroy the planet.