Got challenged by teacher, Coulomb's Law.

[yasu7]

This may not be a challenge for some of you, but it is hard for me as I just got introduced to the topic, your help will be appreciated.
It is about Electric Force. Coulomb's Law.

Homework Statement

Charges of -1 micro coulomb and -4 microcoulomb are placed at opposite ends of a meter ruler. Where on the ruler could...
(a) a free electron be placed and be in electrostatic equilibrium?
(b) a free proton be placed and be in electrostatic equilibrium?

Homework Equations

F=K(q1q2)/r2

F= Force (Newtons)
Q= Coulombs charges
R= distance between the charges
K= botlzmann constant

The Attempt at a Solution

I tried getting the answer by doing math without involving phyisics, like this:If 4 microcolombs is 100%
then 1 microcoulomb might be 25%
and I have a 1 meter long ruler,
then the new coulomb would be placed 25% to the right from the force that has 1 microcoulomb. That would be 25 cms to the right from the -1 microcoulomb

I reach this conclusion by math logic, but I believe it's wrong and my teacher told me it really is wrong, my method is ambiguous so..

I hope someone helps me get me the correct answer.

 

[LowlyPion]

Welcome to PF.

You would be better served to set it up algebraically, where

X = distance to one charge and 1 - X = distance to the other.

Since you want the forces to be equal at that point ... then set them equal and solve for X.

 

[nlightner]

Hello,

Thank you for reaching out for help with Coulomb's Law. It is completely understandable that you find it challenging, as it is a fundamental concept in electricity and magnetism. I am happy to assist you in understanding this law and finding the correct answers to your homework questions.

First, let's review Coulomb's Law. This law states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as F = k(q1q2)/r^2, where F is the force, k is the Coulomb's constant (not the Boltzmann constant), q1 and q2 are the charges, and r is the distance between the charges.

Now, let's apply this law to your homework questions. For part (a), we are looking for a point on the ruler where a free electron can be placed and be in electrostatic equilibrium. This means that the net force on the electron must be zero, so it is not moving. To achieve this, the force from the -1 microcoulomb charge must be balanced by the force from the -4 microcoulomb charge. Since the force between two charges is directly proportional to the product of the charges, we can set up the following equation:

F1 = F2
k(q1q2)/r1^2 = k(q1q2)/r2^2

Since we are only concerned with the distance between the charges, we can simplify this equation to:

r1^2 = r2^2

Now, we know that the distance between the two charges is 1 meter, so we can set up the following equation:

r1^2 + r2^2 = (1 meter)^2

Using basic algebra, we can solve for r1 and r2:

r1 = 0.5 meters
r2 = 0.5 meters

This means that the free electron can be placed at the midpoint of the ruler (0.5 meters) and be in electrostatic equilibrium.

For part (b), we are looking for a point on the ruler where a free proton can be placed and be in electrostatic equilibrium. Using the same logic as part (a), we can set up the following equation:

F1 = F2
k(q1q2)/r1^2 = k(q1q2)/r