# Columb distance/charge balancing problem

• Specialmias
In summary: If the distance from the 0 cm mark is x cm, then the proton must be 30 cm from the +1 charge and 60 cm from the +4 charge.
Specialmias

## Homework Statement

A meter stick has two charges placed on it at the 0 mark is a charge of +1 coulomb. On the 100cm mark is a charge of +4 coulombs. Where should a proton be placed on the meter stick so that the net force due to both charges is 0.

## Homework Equations

Kc = Coulomb const.
Q= charge
a=unknown distance from +1 on proton
b= unknown distance from +4 on proton
X= proton on line
(Kc*Q1*Qn)/r^2= Force 1 on n

## The Attempt at a Solution

So far I've attempted to do the following:
+1_________________+4
The proton must fall in some region between the two.
If we take 50cm to be the origin of this system and 100 to be +50cm and -50 to be the negative maximum the system at 0 then the +1 charge acts on it towards the negative X direction. So it goes from this:

0________100cm
to
-50cm_______0_______50cm

-[(Kc*Qproton*Q+1)/a^2]+(Kc*Qproton*Q+4)/b^2 = 0
This however, gives me:
[b^2/a^2]=4/1
b/a=2/1

Which to me says that in order for this equation to be true then the distance to the proton on the +4 charge must be twice that of the distance from +1. However I can't seem to find any reasonable way to put this on the meter stick. The only possibility I can think of that would follow this is that the proton must be 30cm from the +1 charge and 60cm from the +4 charge but this still leaves 10cm that don't exist on the meter stick.

Have been working on this for a few hours now and am beginning to think maybe I'm thinking about this the wrong way. Any help is greatly appreciated.

Welcome to PF!

Specialmias said:
… in order for this equation to be true then the distance to the proton on the +4 charge must be twice that of the distance from +1. However I can't seem to find any reasonable way to put this on the meter stick. The only possibility I can think of that would follow this is that the proton must be 30cm from the +1 charge and 60cm from the +4 charge but this still leaves 10cm that don't exist on the meter stick.

Hi Specialmias! Welcome to PF!

Yes, you're right … the distance to the proton on the +4 charge must be twice that of the distance from +1.

Now calm down!

just use algebra …

start by saying "if the distance from the 0 cm mark is x cm, then … "

Oh wow. 3X completely whooshed by my head. You've saved my sanity, thank you.

## 1. What is the Columb distance/charge balancing problem?

The Columb distance/charge balancing problem is a concept in physics and chemistry that relates to the forces between charged particles. It refers to the challenge of finding the optimal arrangement of charged particles in space to minimize the total Coulombic potential energy between them.

## 2. Why is the Columb distance/charge balancing problem important?

This problem is important because it has applications in various fields such as materials science, nanotechnology, and biochemistry. Understanding how charged particles interact with each other is crucial for designing new materials, developing efficient energy storage devices, and studying biological processes.

## 3. How is the Columb distance/charge balancing problem solved?

There is no one-size-fits-all solution to this problem as it depends on the specific system and the desired outcome. However, it is often solved using computational methods such as molecular dynamics simulations or density functional theory calculations. These methods use mathematical algorithms to determine the optimal arrangement of charged particles based on their properties and the surrounding environment.

## 4. What are some challenges associated with the Columb distance/charge balancing problem?

One of the main challenges is the complexity of the interactions between charged particles. In many cases, the Coulombic potential energy cannot be solved analytically, and therefore, numerical methods must be used. Additionally, the presence of other factors such as solvent molecules or external electric fields can complicate the problem further.

## 5. How does the Columb distance/charge balancing problem relate to other concepts in science?

This problem is closely related to other concepts such as electrostatics, chemical bonding, and molecular structure. It also has connections to other branches of physics, including quantum mechanics and statistical mechanics, as it involves the interactions between particles at the atomic and molecular level. Furthermore, the solution to this problem can provide insights into the behavior of systems at different length scales, from the nanoscale to the macroscale.

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