Electrostatic force including coulombs law

[th3plan]

Homework Statement

Of the charge Q initially on a tiny sphere, a portion q is to be transferred to a second, nearby sphere. Both spheres can be treated a particles. For what value of q/Q>0.5 will the electrostatic force between the two parts have 1/2 of the maximum possible value?

The Attempt at a Solution

ok i drew a picture and i know that sphere 1 is Q-q , and sphere 2 is q, and i plug into equation

F=k(Q-q)q/r^2

i differentiate and get qQ-2q now what i do from here, to get 1/2 maximum possible value

i know to get maximum i set equal to zero, do i set this equal to 1/2? How would i solve it for q/Q ratio if its equal to 1/2?

 

[granpa]

Q is a constant. just set it equal to 1. same with r.

 

[baba89]

I would like to offer some clarification on the content being discussed. The electrostatic force, as described by Coulomb's law, is a fundamental force that exists between electrically charged particles. It is responsible for many phenomena in our everyday lives, such as the attraction and repulsion between objects, the functioning of electronic devices, and the behavior of atoms and molecules.

In this homework problem, we are dealing with the transfer of charge between two tiny spheres. The electrostatic force between these spheres can be calculated using Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Now, to determine the value of q/Q that will result in the electrostatic force being half of its maximum possible value, we can set up the following equation:

F = k(Q-q)q/r^2 = 1/2 * kQ^2/r^2

This equation represents the electrostatic force at half its maximum value, where k is the Coulomb's constant and r is the distance between the spheres. To solve for q/Q, we can rearrange the equation and get:

q/Q = (2r^2 - 1)/(2r^2)

Therefore, for q/Q to be greater than 0.5, the value of r must be greater than 1/sqrt(2) or approximately 0.707. This means that the distance between the spheres must be less than 1.414 times the radius of each sphere.

In conclusion, Coulomb's law allows us to calculate the electrostatic force between charged particles, and by setting the force equal to half of its maximum value, we can determine the ratio of charge transfer needed for that force to occur. This can be useful in understanding and predicting the behavior of charged particles in various situations.