AP® Physics 2: Algebra-Based · Unit 10 · Topic 10.1
Comparing the Electric and Gravitational Forces
The electric force and gravity both follow an inverse-square law, but they come from different properties of matter, charge versus mass, and the electric force is vastly stronger for charged particles at the same scale.
A charged comb can lift a scrap of paper against the pull of the entire Earth because the electric force between the comb and the paper's charges is enormously larger than the gravitational force between the paper and the whole planet. It isn't that the comb is special. It's that the charge-to-mass ratio of the paper's electrons and protons makes the electric interaction dominate completely once any charge imbalance exists.
Coulomb's law, Fe = kq_1q2/r2, and Newton's law of gravitation, Fg = Gm_1m2/r2, have identical shapes: both drop off as one over the square of the separation, and both depend on a product of two source quantities times a constant. That shared shape comes from the same geometric fact, that influence spreads out over a spherical area proportional to r2, whether the influence is 'charge-ness' or 'mass-ness'. But the sources themselves are completely different. Mass only attracts. Charge can attract or repel, because charge comes in two signs and mass effectively comes in only one.
Because both forces share the 1/r2 dependence, their ratio Fe/Fg at any separation simplifies to (k/G) times (q/m)2, with the distance canceling out entirely. This sets up the next idea in the unit: the electric field. Since Fe and Fg have the same geometric skeleton, you can strip the second particle's property out of each and define a field, electric or gravitational, that exists at a point in space independent of whatever charge or mass you bring in to test it.
Key terms
- Coulomb's law
- Fe = kq_1q2/r2, the force between two point charges, attractive or repulsive depending on their signs.
- Newton's law of gravitation
- Fg = Gm_1m2/r2, the always-attractive force between two masses.
- Inverse-square law
- A relationship where force or influence falls off in proportion to one over the square of the distance from the source.
- Charge-to-mass ratio
- The quantity q/m for a particle, which determines how strongly electric force competes with gravity for that particle.
Watch it explained
- How it worksHow do Coulomb's law and Newton's law of gravitation end up with the exact same shape?
- Worked exampleFind the ratio of the electric force to the gravitational force between two protons.
- Common mistakeWhy isn't gravity simply a weaker version of the electric force?
- Going furtherWhat changes about a two-particle problem when both charge and mass matter at once?
Check yourself
End of topic.