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When two unlike charged particles are placed at a distance they get attracted but the force depends on the inverse of the square of distance between the particles. So when they approach each other (as d becomes 0) wont their velocities become very huge and when they collide wont the d between them become 0 so the force will be infinite. Or maybe the law is not valid in microscopic terms?

Similarly with the gravitation law.....when we touch something (feel something), do we actually feel the force as distance between hands and object tends to 0? That would mean nothing is in contanct with anything in the universe.

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To the first question, yes. Two particles with opposite charges will attract, and if the electromagnetic force was the only force in the universe, AND the particles start off as either stationary or on the exact right trajectory to collide, the two will collide.

It should, however, be noted that if the trajectories are even slightly off, the two particles will wind up in eliptical orbits around one another. Additionally, it should be noted that the weak nuclear force is repulsive, and much stronger at short distances.

For the second question, 'touching' is ill-defined in physics, especially when you consider that a particle like the electron is, by most, considered to be a point. What we consider touching in daily life is nothing other than a combination of forces keeping you from pushing your hand straight through, say a block of wood.

Edit: Note that at the distance we typically experience as 'touch', the gravitational pull between the surface of the object and your finger is still negligible compared to the repulsive forces between the two.

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