Newton's law of gravity and Coulomb's law of electric force share a strikingly similar mathematical structure: both describe a force between two objects that falls off with the square of the distance between them — double the distance, and the force drops to a quarter of its previous strength, in both cases. Despite that shared shape, the two forces differ by an almost unimaginable factor in raw strength, and that difference in magnitude, not the shape of the law itself, is what determines which force actually dominates at different physical scales.
Two forces, the same inverse-square shape, wildly different strength
Coulomb's law states that the electric force between two charged objects is proportional to the product of their charges and inversely proportional to the square of the distance between them — mathematically, the same basic inverse-square relationship Newton's law of gravity describes for masses instead of charges. But the constant that scales Coulomb's law is vastly larger than the equivalent constant in Newton's law of gravity, meaning that for two particles carrying a typical elementary charge, the electric force between them at a given distance is dramatically stronger, by dozens of orders of magnitude, than the gravitational force between two particles of comparable mass at the same distance. Both laws share an identical mathematical shape; only the sheer scale of the force involved differs, but that scale difference turns out to be enormous.
Why gravity still wins at the scale we actually notice it
Given how dramatically stronger the electric force is compared to gravity, it might seem strange that gravity, not electric force, is what visibly governs the motion of planets and the fall of everyday objects. The reason comes down to a key structural difference between charge and mass: electric charge comes in both positive and negative varieties that attract and repel, and ordinary bulk matter is, overall, extremely close to electrically neutral, with roughly equal amounts of positive and negative charge that cancel out at any meaningful distance — meaning the enormous electric forces between individual charged particles mostly cancel each other out when you're looking at two large, roughly neutral objects like planets. Mass, unlike charge, comes in only one variety and always attracts, with no equivalent cancellation, which is why gravity, despite being astronomically weaker force-for-force between any two individual particles, ends up dominating the large-scale motion of astronomical objects, while the electric force, despite being far stronger at the level of individual charged particles, dominates instead at the atomic and molecular scale, where charge neutrality doesn't cancel things out the same way.
What we're still unsure about
The mathematical form of Coulomb's law, its shared inverse-square structure with gravity, and the enormous disparity in relative strength between the two forces are all extremely well established, precisely measured physics with no genuine scientific dispute. What remains one of the deepest open questions in fundamental physics is why the universe's fundamental forces have the specific relative strengths they do at all — physicists don't currently have a full, from-first-principles explanation for why gravity is so many orders of magnitude weaker than electromagnetism, sometimes called the hierarchy problem in particle physics, and it remains an active area of theoretical research rather than a settled, well-understood result.
This sits inside Electric Charge & Coulomb's Law, one of eight topics in Electromagnetism, one of five domains in Physics, one of seventeen subjects the app can quiz you on.