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How are the gravitational and electric force comparable?

  1. Dec 21, 2012 #1
    I hear all the time how the electric force is so much stronger than gravity.

    I understand both forces are inversely proportional to the distances squared, and that the gravitational constant is roughly 10^20 times greater than the coulomb constant.

    But one involves charges, while the other involves mass. To me this makes as much sense as a saying a second is larger than a meter. What am I not understanding?
  2. jcsd
  3. Dec 21, 2012 #2
    First, Coulomb constant is approximately 10^20 times greater than the gravitational constant, not the other way around :)

    Yes, the quality of objects is different, but you are comparing resulting force between them. Eventhough the forces have different natures, the value you can read on your imaginary force meter when comparing is of the same kind.
  4. Dec 21, 2012 #3


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    Try working out the electric and gravitational forces acting on a pair of electrons....


  5. Dec 21, 2012 #4
    Dot4: ha, yeah that's what I meant. Switching them was a typo.

    Why is it less valid to give the Earth and moon some small charge and then compare the electric and gravitational forces acting between them?

    You would probably say oh well the mass in this case is so much greater than the charge. But that brings me back to my original question of asking how is that different than comparing a second and kilogram.
  6. Dec 21, 2012 #5


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    seconds and kilograms don't measure the same thing. Electrostatic force is a force and gravitational force is a force --- they are the same thing in that sense. What part of that do you not understand?
  7. Dec 21, 2012 #6
    Well what I mean is that coulombs and kilograms don't measure the same thing. Gravity wins in the moon/earth scenario because the mass is so much greater than the charge. That last part compares coulombs and kilograms, right?
  8. Dec 21, 2012 #7


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    When you think about it, you should realise that both coulombs and kilograms are in the same category of "things", but seconds and kilograms are not.
    Mass and charge are properties of elementary particles that are the source of attractive forces. These similarities let you compare the two, by e.g.looking at the differences in strength of the force they produce, or observing which elementary particles have which property.
    You can't draw such parallels with time and mass. They're completely different.

    To use an analogy: You might be attracted to person's eyes or singing ability. Hence you can talk about what turns you on more, and which person has got better voice or more charming eyes.
    You can't really compare any of those two with days of the week.
  9. Dec 21, 2012 #8
    Just to add to Bandersnatch's explanation. Even in the case of earth and moon, were both made of the same kind of electricity, you could measure how much electric force is bigger than gravitational. They are both measured using the same properties.
  10. Dec 21, 2012 #9
    This is the source of your confusion. You should say one involves charge, which is the electromagnetic force, and one involves gravitation, which is the gravitational force.

    Now it should be clear that you are comparing forces, and you can proceed from there. A force is that which changes momentum.

    When a charge (electromagnetic force) changes the momentum of an object, this momentum change is applied to the mass of the object. You see, an electron is not just about charge, it has mass too. I think that is a good way to think about charge. Charge is not directly relating to the motion of the particle, but rather think of charge in terms of the process which changes the momentum of the particle.

    BTW, there are really only four forces in nature, gravitation, electromagnetic, weak force, and strong force (or three if we accept that the electromagnetic and weak force have been unified into the electro-weak force). When we speak of applying a force to an object, say throwing a ball, what force is that? It might at first seem as if this is a different kind of a force, but really it's not. The contact forces between your hand and the ball are electromagnetic. There are also forces from your muscles which are originated from the chemical processes in your body which ultimately are electromagnetic.
  11. Dec 21, 2012 #10


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    Imagine a magnet. You can pick up another magnet with it and both will easily overcome gravity. The same thing applies for electric charge. With a very very small portion of an objects electrical charges out of balance you can pick up another electrically charged object. Just a small percentage of charges added or missing from an object completely dominates the force of gravity from the entire Earth! That's what is meant by saying electromagnetism is much stronger than gravity.
  12. Dec 21, 2012 #11
    Are you familiar with the term "active gravitational mass"? It is sometimes referred to as "gravitational charge", and is also called "the standard gravitational parameter". It is defined by Kepler's third law:
    Notice that mass is not in there anywhere. It just so happens that [itex]\mu[/itex] and mass are proportional.
  13. Dec 21, 2012 #12


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    What's meant mathematically is that the dimensionless coupling constant describing the electromagnetic force is much larger than that describing the gravitational force.

    The thing is, we can unambiguously define an electromagnetic coupling constant (the fine structure constant, ~ 1/137), because there is a unique smallest electric charge.

    There's not a unique smallest mass, as each elementary particle has a different mass which does not appear to be related to any fundamental mass unit. So you get a different gravitational coupling constant depending on which fundamental particle you pick. But regardless of which one you pick, you always get an answer which is many orders of magnitude smaller than the electromagnetic coupling constant.
  14. Dec 22, 2012 #13
    Wait a minute. Is the gravitational coupling constant actually different per unit of mass, for different particles? It seems strange to me because I normally think of gravitational force in terms of mass, without regard to what kind of mass it is.

    Let me rephrase that question. Would a gram of electrons (if they could be held together for a time) have the same gravitation force as a gram of protons, even if both have a different gravitational coupling constant?

    Also, in the Wikipedia article about the gravitational coupling constant, it says that the gravitational coupling constant characterizes the gravitational attraction between charged elementary particles having nonzero mass. Can you please explain a little about the relationship with gravitation and charge, because I have previously thought that they were unrelated?


    P.s. What about a gram of neutrons. Neutrons are not charged so they might be excluded from having a gravitational coupling constant, yet they have mass and definately exert gravitational influence. Perhaps they are able to have GCC based on the fact that they are composed or quarks, which do have charge?
    Last edited: Dec 22, 2012
  15. Dec 22, 2012 #14
    The electron and the proton are the basic building blocks of all objects in the universe, so the Earth and the Moon are just a bunch of electrons...The difference being that there is positive and negative charge, and so the electric force is screened out over large distances, whereas gravity is not.

    Think of the amount of mass required to generate a gravitational pressure needed to overcome the electromagnetic binding force between molecules inside the mass--the equilibrium occurs, basically, when an object in space becomes spherical. This happens at about 1020 - 1021kg. Divided by the mass of a proton implies you need about 1047 atoms to generate the amount of gravitational pressure to break the electromagnetic strength between atoms. This should hopefully demonstrate to you why comparing gravity vs. electromagnetic forces between an electron or proton is not such an arbitrary method of determining the relative strength of the two forces.
    Last edited: Dec 22, 2012
  16. Dec 22, 2012 #15


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    My point is this, the dimensionless gravitational coupling constant is given by
    [tex]\alpha_G = \frac{G m_1 m_2}{\hbar c} = \frac{m_1 m_2}{m_p^2}[/tex]
    So while the Newton gravitational constant G is a fundamental constant of nature, [itex] \alpha_G[/itex] depends on [itex] m_1 [/itex] and [itex]m_2 [/itex]. The reason is, as I said, there is no 'fundamental unit of mass' as there is a fundamental unit of charge.

    Of course the force of gravity is given by the usual F=GmM/r^2, which doesn't care at all about composition.

    I think the only reason they mention charged particles is to compare to the fine structure constant, which is defined of course in terms of electrical charge. I see no reason why you can't have a gravitational coupling constant for neutral particles.
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