Solve Coulomb's Law 1D: Find q3 for Zero Force

In summary, the three charges must be placed so that the resultant force on them is zero. The positive charge q3 must be placed left of the origin (-x).
  • #1
Mitchtwitchita
190
0

Homework Statement



Three charges lie along the x-axis. The positive charge q1 = 10.0 x 10^-6 C is at x = 1.00 m, and the negative charge q2 = -2.00 x 10^-6 C is at the origin. Where must a positive charge q3 be placed on the x-axis so that the resultant force on it is zero?

Homework Equations



F=kq1q2/r^2

The Attempt at a Solution



F23 = -F13

F23 = k(-2.00 x 10^-6 C)q3/-x^2
F13 = -k(10.0 x 10^-6 C)q3/(1.0 m - x)^2

[k(-2.00 x 10^-6 C)q3/-x^2] - [k(10.0 x 10^-6 C)q3/(1.0 - x)^2] = 0
(-2.00 x 10^-6 C)/-x^2 = (10.0 x 10^-6 C)/(1.0 -x)^2
2/x^2 = 10/(1- x)^2
2 - 4x + 2x^2 = 10x^2
-8x^2 - 4x +2 = 0

My quadratic equation doesn't work out so I'm assuming there was a terrible malfunction earlier on. Can somebody please help me out with this one?
 
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  • #2
Hint: First figure out what region the positive charge q3 must be in. ( x < 0; 0 < x < 1; x > 1) The field from each charge may have a different sign in different regions, which affects how you'd write the equation.
 
  • #3
It's going to be left of the origin (-x). How would this affect my initial signs?
 
  • #4
Mitchtwitchita said:
It's going to be left of the origin (-x). How would this affect my initial signs?
Actually your equations are fine. (I just saw the double negative.) Why do you think your quadratic doesn't work out?
 
  • #5
Because I end up with 4 +/- sqr.[(-4_^2) - (4)(-8)(2)]/2 x 2
= (4 - 80)/4
= -19 which is much too high.
 
  • #6
Er, I meant low in the last reply.
 
  • #7
Mitchtwitchita said:
Because I end up with 4 +/- sqr.[(-4_^2) - (4)(-8)(2)]/2 x 2
= (4 - 80)/4
= -19 which is much too high.
I assume you are trying to use the quadratic formula. Try again; you're making an error somewhere.

Edit: You forgot to take the square root.
 
  • #8
Is my error in the use of the quadratic formula or in the work leading up to it?
 
  • #9
Mitchtwitchita said:
Is my error in the use of the quadratic formula or in the work leading up to it?
Your work is fine. You just forgot to take the square root. (See my last post.)
 
  • #10
Oooooooooh...duh. Thanks!
 

1. What is Coulomb's Law in 1D?

Coulomb's Law in 1D is a mathematical equation that describes the force between two charged particles in one-dimensional space. It is based on the principle that like charges repel each other and opposite charges attract each other.

2. How do you solve Coulomb's Law in 1D?

To solve Coulomb's Law in 1D, you need to know the values of the charges of the two particles, the distance between them, and the value of the Coulomb constant. Then, you can plug these values into the equation F= k*q1*q2/d^2, where F is the force, k is the Coulomb constant, q1 and q2 are the charges, and d is the distance between the two particles.

3. What is q3 in the context of solving Coulomb's Law in 1D?

In the context of solving Coulomb's Law in 1D, q3 refers to the unknown charge of a third particle that is placed in the vicinity of the two charged particles. The goal is to find the value of q3 that will result in a zero net force on the system.

4. Why is finding q3 for zero force important in Coulomb's Law in 1D?

Finding q3 for zero force is important in Coulomb's Law in 1D because it allows us to understand the equilibrium point of the system. This means that the net force on the system is zero, indicating that the forces between the three particles are balanced and there is no movement or acceleration.

5. Are there any real-world applications of solving Coulomb's Law in 1D?

Yes, there are many real-world applications of solving Coulomb's Law in 1D. This law helps us understand the behavior of electric charges, which is essential in fields such as electronics, engineering, and physics. It is also used in designing electrical circuits, determining the strength of electric fields, and predicting the movements of charged particles in space.

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