HoW is Coulombs law similar to newtons law?

Answer 1

They are algebraically (mathematically) identical.

Both laws say that the force between two objects is proportional to the product
of how much of the same thing each one has, and inversely proportional to the
square of the distance between their centers, and that it acts along the line
between their centers.

The property that Coulomb's Law is interested in is electric charge, and Newton's Law
is interested in mass instead.

Past that, you can massage both Laws with the same operations from Geometry and
Calculus, and you get all the same kind of results ... pairs of equal, opposite, mutual forces
between two objects, acceleration, escape velocity, elliptical orbits around each other, etc.
With one highly-charged ping-pong ball and a bunch of slightly-charged ones, you could
set up a working model solar system that followed the laws of Newton and Kepler both.

The one giant, glaring difference is that with electric charges you can have forces
that either pull together or push apart, but, as far as we know now, with masses
you can only get attraction.

But that's a difference between charge and mass. It's got nothing to do with the Laws.
The laws are still identical.

Answer 2

Coulomb's law and Newton's law of universal gravitation are both inverse square laws that describe the force between two objects. Coulomb's law deals with electric forces between charged particles, while Newton's law addresses gravitational forces between masses. Both laws involve a constant of proportionality, the product of the two charges or masses, and the inverse square of the distance between them.