Solving Electrostatics Question: Third Charge Placement for Zero Net Force"

[RexPokinghorn]

Wow, it's been a long time since I've done any physics, but my sister asked me for help on a question and I am stumped.

The problem is:

A +2.7 micro coulomb and a -3.5 micro coulomb charge are placed 25 cm apart. where can a third charge be placed so that it experiences no net force?

What I remember is since the two charges have different signs, the third charge must be placed outside of the other two. It cannot lie in-between the other two.

Other than that... I'm drawing a blank. Any help / helpful hints would be much appreciated!

 

[arcnets]

Originally posted by RexPokinghorn
What I remember is since the two charges have different signs, the third charge must be placed outside of the other two.

Great! That's correct physical thinking, in my opinion. Another idea is that, as a consequence of symmetry, the desired position must lie on the line connecting the 2 charges. Now, since the force decreases with distance, the desired position must be further away from the big charge than fom the small charge. To solve, remember the 'inverse square law'...

 

[M98Ranger]

Sure, I'd be happy to help! Solving electrostatics problems can be tricky, but with some basic principles and equations, we can figure out the answer to this question.

First, let's review the basics. Coulomb's 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 written as F = k * (q1 * q2)/r^2, where k is a constant and r is the distance between the charges.

In this problem, we have two charges, +2.7 micro coulomb and -3.5 micro coulomb, placed 25 cm apart. We want to find the location of a third charge where it experiences no net force.

To solve this, we need to use the principle of superposition, which states that the net force on a charge is the vector sum of the individual forces acting on it. In other words, we need to find the location where the forces from the two charges cancel each other out.

To do this, we can set up an equation using Coulomb's Law. Let's call the third charge q3 and the distance between it and the +2.7 micro coulomb charge as x, and the distance between it and the -3.5 micro coulomb charge as (25-x). This is because the total distance between the two charges is 25 cm, and we are assuming that the third charge is placed somewhere between the two charges.

So, our equation becomes:

F = k * (q1 * q3)/x^2 - k * (q2 * q3)/(25-x)^2

Since we want the net force to be zero, we can set this equation equal to 0 and solve for x:

0 = k * (q1 * q3)/x^2 - k * (q2 * q3)/(25-x)^2

Solving for x, we get x = 25 * (q1/q2)^(1/2)

This means that the third charge should be placed at a distance of 25 * (q1/q2)^(1/2) cm from the +2.7 micro coulomb charge in order to experience no net force.

I hope this helps! Remember to always use the principles and equations we have learned in class to solve problems like this