# Finding the force of attraction between a neutral and charged object

I have looked through similar questions on stack exchange but I cannot find an answer that is satisfying my curiosity. Before getting into the question, I will make it painfully clear that I only have a basic understanding of physics and mathematics. While I have dabbled in self study to calculus, pre-calculus, and more complex physics, my conventional education only reaches the level of intermediate algebra and high school level physics. Now, as for the question. It just came to my understanding after reviewing induction that a force of attraction or repulsion could occur between a neutral and charged object. I visualized it as a drawing of two objects displaying the polarization of the charges. So I came to the conclusion that it would be solvable with Coulombs law. To avoid going on a tangent I will simplify the question.

Imagine a simple diagram consisting of one object A distance x away from object B. Object A shall be positively charged and B neutral. Call A's charge y. Now, assume object B is highly or even perfectly conductive. (I believe this property should allow for the free movement of electrons) Now because of this, the electrons will move toward the side of object B closest to object A. Therefore causing a difference in charge of the two sides. There would be a force of attraction between the closer "negative" side of B, but also force of repulsion from the farther "positive" side of B. Now the problem that arises here is simple yet I do not know how to approach it. Say we make a set of equations to label this using Coulomb's law. Doing this we find that the Net force will be equal to the sum of the force of attraction and repulsion. Now the problem in finding this (assuming we have the charges of these sides) lies in the distance. There will be some finite distance difference between the "positive" and "negative" sides in B. This is what allows some force of attraction between charged and neutral objects. So the real question comes now. How do you find this finite distance that would allow you to calculate the force of attraction/repulsion. Finding the charge is a problem on its own but I am interested in seeing how you could find the distance in order to calculate the charge.

This image I found online summarizes the question well. [Electron Movement in Conductors]

If you view this image you will see the difference in distance I am talking about. How could you calculate this. I am on a time crunch writing this and will clarify anything if needed.

• Linked, as well as. Commented Apr 21, 2022 at 18:27
• The basic answer to your question "How do you find this finite distance that would allow you to calculate the force of attraction/repulsion?" is "You use calculus to sum up all of the contributions from the charges at all different distances." However, there may be other shortcuts for the specific case of spherical objects (such as the one described in @Mike's answer.) Commented Apr 21, 2022 at 19:14