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How are the gravitational and electric force comparable? 
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#1
Dec2112, 03:55 AM

P: 113

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
Dec2112, 04:41 AM

P: 2

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. 


#3
Dec2112, 06:30 AM

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http://www.schoolforchampions.com/...ctrostatic.htm 


#4
Dec2112, 09:49 AM

P: 113

How are the gravitational and electric force comparable?
Dot4: ha, yeah that's what I meant. Switching them was a typo.
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. 


#5
Dec2112, 10:10 AM

PF Gold
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#6
Dec2112, 10:18 AM

P: 113




#7
Dec2112, 10:39 AM

P: 739

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. 


#8
Dec2112, 12:13 PM

P: 211

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.



#9
Dec2112, 04:44 PM

P: 211

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 electroweak 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. 


#10
Dec2112, 04:49 PM

Mentor
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#11
Dec2112, 05:02 PM

P: 759

[tex]\mu=4\pi^2R^3T^{2}[/tex] Notice that mass is not in there anywhere. It just so happens that [itex]\mu[/itex] and mass are proportional. 


#12
Dec2112, 07:11 PM

Sci Advisor
P: 2,193

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. 


#13
Dec2212, 06:35 PM

P: 211

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? Thanks. 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? 


#14
Dec2212, 07:06 PM

P: 398

Think of the amount of mass required to generate a gravitational pressure needed to overcome the electromagnetic binding force between molecules inside the massthe equilibrium occurs, basically, when an object in space becomes spherical. This happens at about 10^{20}  10^{21}kg. Divided by the mass of a proton implies you need about 10^{47} 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. 


#15
Dec2212, 11:42 PM

Sci Advisor
P: 2,193

[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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