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The force is weak with this one… June 16, 2011

Posted by mareserinitatis in electromagnetics, geology, geophysics, physics, science.
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I had an interesting question from someone today: why do we use electromagnetics to study so many things?  Why can’t we use gravity or something similar?  Specifically, they were wondering about non-invasive methods for studying the human body.

It’s easiest to start with Newton’s Law of Gravitation, which tells us how much gravitational force one object (M) exerts on another (m):

and Coulomb’s Law (which explains the force of attraction between electrical charges, Q and q):

If we want to find the ratio of gravitational force to electrical force, we end up with something like this:

Now, let’s imagine we’re just looking at the gravitational and electrical forces between two electrons from 1 m away.  We use G=6.673•10-11 m3 kg-1 s-2 (the gravitational constant), M=m=9.11•10-31 kg (the masses of the two electrons), εo=8.854•10-12 C2 kg-1 m-3 s2 (the permittivity of free space, although may be just as easy to think of it as an electrical constant), and Q=q=1.602•10-19 C (this being the charge of an electron).  Using these values, all our units will disappear, which is good because we’re looking at a ratio of two forces and shouldn’t have any units, and we end up with a value of about 2•10-43.

What this means is that the gravitational force is 43 orders of magnitude smaller than the electrical force…or you could put a decimal point with 42 zeros and then a 1 behind it, and that’s how much smaller the force is.  When it’s already difficult to measure current values that contain many, many electrons (as compared to the two electrons we examined), it’s going to be impossible to find something that exerts a force that is 43 orders of magnitude smaller than what we can already pick up.

You can pick up small changes in gravitational forces when talking about large geophysical features – like ore deposits and mountain ranges.  In fact, they use this principle a lot in exploration geophysics, where they use gravimeters to look for mineral resources.  Our bodies are less sensitive than that, though, and can only pick up gravity when we are talking about changes in the size of planets or moons.  However, we are sensitive to changes in acceleration, so you can feel changes in gravitational pull when riding on an elevator, but that is because the change is both fast and of a reasonable size.

Anyway, the huge difference is why we are permeated (ba dum ching!) by devices that detect and use changes in electromagnetic radiation but not in gravitational energy.

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Comments»

1. Jacob - June 24, 2011

I think there’s other reasons too. One of them is that gravity only has a single “charge” that attracts, whereas electricity has two charges that attract and repel, and can exhibit all sorts of more interesting behaviours. With gravity it’s hard to do anything other than just clump things up into a sphere, or put two things in orbit around each other, because that’s the nature of a universally attractive force. Even the very sensitive gravity probes use electronic sensors to measure disturbances in a test mass, because you can’t really make any kind of “device” operating just on gravity. Basically, I don’t think we will have any “Gravitronic” devices in the future, and it’s not only because the force is so weak =)

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mareserinitatis - June 24, 2011

I think the biggest problem is actually that there’s no good way to sense gravity without a very large object. Electromagnetism is easy to pick out because of the fact that you can mobilize electrons and they can do cool things with very low energy. Gravity has no such counterpart – in order to detect it, you need to have another significant mass. In a lot of the sensors we make, most of the behavior we pick up is actually a change in the current or fields from the current, which most often doesn’t have anything to do with repulsive charges. (Although you’re right that the potential for interesting behaviors is definitely more present with emag.)

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