# Electrical force vs gravitational force

Given that the electrical force is so much stronger than gravitational force at atomic levels, why is it that it's the gravitational force between you and the earth that keeps you on the ground rather than the electrical force between you and the earth?

• hint: which electrical force? – Tobias Kienzler Jan 25 '11 at 7:03
• Please note that the "homework" tag does not solely indicate problems that someone is actively trying to solve for their next problem set. Problems for exam review or problems encountered in a textbook during independent study are also considered "homework" meta.physics.stackexchange.com/questions/234/… – Mark Eichenlaub Jan 25 '11 at 8:54
• Nope not studying for an exam either-semester just started. I was intrigued by something so I asked it. Apparently WIMP is the only one that really knew the answer-the rest of you guys just spent all your time trying to argue rather than answering questions. You lose nothing by answer this question whether its homework or not. Obviously you guys are just trying to argue about something and attempt to gain authority over this site. Last I checked it was run by the community. I am part of the community. If I claim its not homework, then its not homework. – Snowman Jan 25 '11 at 21:28
• The tags are not for your benefit. They're for everyone else's benefit as they sort through the questions. That means the questions should be tagged according to their content, not according to the asker's whim. Regardless, this has become a meta discussion so if you want to continue it, we should do it on the meta site. – Mark Eichenlaub Jan 26 '11 at 9:16

## 3 Answers

Gravitational force is what keeps us on the ground rather than electrical force because there's no negative gravitational mass. Electric charge can be neutralized, while gravitational attraction not.

Actually, if you were at rest on the ground, the van der Waals repulsion between the atoms of the soles of your feet and the atoms of the ground — which is electrical in origin — exactly cancels the gravitational force between your entire body and the entire mass of the Earth.

Imagine that!

And the van der Waals force isn't even a direct Coulomb force between two simple charges, but a much weaker indirect electrical repulsion between neutral atoms due to a deformation of the electron clouds. I know you might argue the repulsive van der Waals force is actually due to the Pauli exclusion principle, and that is also true. After fixing the positions of the nuclei, the physical ground state — which is given by a totally antisymmetric electron wavefunction — has a higher energy than some unphysical electron wavefunctions which aren't totally antisymmetric. But if we restrict ourselves to the physical wavefunction, the immediate repulsive force can still be traced back to electrostatics.

You write "rather than the electrical force between you and the earth". There is no electrical force between you and the earth because neither of you is charged! But you and the earth do both have mass so gravity acts but electricity doesn't.

"that the electrical force is so much stronger than gravitational force at atomic levels'" is only true between two charged particles of say the mass of a proton and the charge of a proton.

## protected by ACuriousMind♦Nov 15 '16 at 17:25

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