# Electrostatic force and their affect on 3D objects

So I am new to this science forum so please have mercy. I just have some basic questions about electrostatic forces. I hope these are not too vague. So basically from my understanding, if you have two oppositely charged particles, the opposites will attract due to the electrostatic force. The strength of force is predicted by Coloumb’s law. My question is can these charged particles also be charged objects? And when they attract and meet, is there a formula for the speed and time that they would take to be joined together? I want to understand the affect of the electrostatic force on objects. So basically if you had two 10 x 10 x 10 micron cubes of matter, each of the opposite charge, what would be the properties of their connection and attraction? I am trying to test out many ideas that I have and I need a firm understanding of electrostatics. I'm sorry if I am vague. Are there any good tutorials and software simulations online?

• Yes the charged 'particles' can be large objects. However, as they get close together, you can no longer treat them each as single points but rather have to integrate Coulomb's law over their entire bodies. – lemon Jan 27 '17 at 18:38

## 1 Answer

As @lemon pointed out in the comment, Coulomb's law (which is the fundamental law of electrostatics) only holds for point charges. But you can divide the object into very small parts and then those tiny parts are now infinitesimal and like points. Then you can integrate the force on each of them.

Fortunately, things are easier with the concept of electric field. Each charges object has an electric field around it. Now if any point charge is placed in the field area, it will feel force. And that force is only related to the electric field at that point and the charge of the particle.

So you can first find the electric field of the first object, and then sum up the forces on the second one. I am not gonna provide any formula, because they presume knowledge of Electromagnetism and Vector calculus.

An special case is when both objects have spherical symmetry. That is there charge distribution at any point on them, only depends on the radius. At this special case a mathematical theorem called Gauss's law can help us simplify calculations. At this condition, both objects can be regarded as point charges at their centers. And the charge of the point charges are equal to the total charge of the object. Now, you can use Coulomb's law.