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Free electrons in a metal are attracted by gravity towards Earth. So why don't they lay down to the bottom of the conduit, like sediment at the bottom of a river?

Qmechanic
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Kevin
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2 Answers2

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Electrons have a negative electric charge, which means they repel other negative charges. Once electrons start to fall to the bottom of the conductor, there will be a greater accumulation of negative charges at the bottom of the conductor than the top. The accumulation of negative charges at the bottom will repel the other free electrons above them, stopping any further accumulation. Because the electric force is so much stronger than gravity, it takes very little movement of electrons to stop any further settlement. So little, in fact, that the difference in the density of electrons between the top and bottom of a conductor is undetectable.

Mark H
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    "Once electrons start to fall to the bottom of the conductor" But they wont because the gravitational force is simply not strong enough. – joseph h Sep 02 '21 at 04:32
  • @josephh Imagine a conductor in deep space, away from any gravitational influence. The charges will take on some distribution based on the shape of the shape. This will be an equilibrium since all electrons will experience a net zero force from the other charges. Now, place this conductor on the surface of a planet. The electrons will now be feeling a net force due to the influence of gravity. Because there is a net force, the electrons will move, but it will take microscopic amounts of movement before the new distribution of charges changes electric field to counteract gravity. – Mark H Sep 07 '21 at 14:15
  • Of course. But the gravitational force is so laughably weak in comparison, that there are zero electrons moving down away from each other due to gravity to begin with, which sort of makes your argument moot. As I stated, the electrical force is $1000000000000000000000000000000000000000$ times stronger than gravity. Even though the electrons in a conductor are free to move, the net electrical charge in their region is zero, and as soon as even one electron is displaced slightly by gravity, – joseph h Sep 08 '21 at 01:06
  • Cont’d> there will be an immediate polarisation which will instantly disappear as the electrostatic force brings the system back into equilibrium. If that is your point, I agree. My point is that such a thing cannot happen to begin with, due to the relative strengths of the forces. – joseph h Sep 08 '21 at 01:07
  • If we were talking about free electrons in a gravitational field moving, then yes, even if the force is very small. But here, electrons bound to a conductor with attractive forces due to positively charged nuclei, will not have any freedom to move “down” such that the effect is to cause polarisation. – joseph h Sep 08 '21 at 01:18
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This is because the gravitational force acting on electrons is significantly weaker than the electric forces that keep them attached to nuclei in atoms.

In fact, the ratio of the electrostatic force to the gravitational force between a proton and an electron works out to be $$\frac{F_e}{F_G}= {\large\frac{k\frac{q_e q_p}{r^2}}{ \frac{Gm_em_p}{r^2}}}= \frac{kq_e^2}{Gm_e m_p}\approx 2.27\times 10^{39}$$ meaning the electric force is about $10^{39}\times$ stronger than the gravitational force.

This means that electric forces will keep the electrons from "falling" anywhere.

joseph h
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  • Can we apply Newton's gravitational force equation for subatomic particles like electron? I mean, the electron is no longer localised like a classical point particle. – KP99 Sep 02 '21 at 09:03
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    Sure we can. The electron still has a mass, albeit very small. – joseph h Sep 02 '21 at 09:07