Coulomb's Law, what charge will make the two charges in static eq.

In summary, to find the charge q1 that will put charge q2 in static equilibrium with the charge Q = -3.7 nC in the middle, we use the equation F = (K*q1*q2)/(r^2) and set it equal to 0. This leads to q2 = 4*Q, or q1 = 4*Q, with the opposite sign.
  • #1
rocapp
95
0

Homework Statement


In the figure below the charge in the middle is
Q = -3.7 nC. For what charge
q1 will charge q2
be in static equilibrium?

Homework Equations


F = (K*q1*q2)/(r^2)

The Attempt at a Solution



I'm not sure where to go after acknowledging that Fq1->q = -Fq2->q
 

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  • #2
rocapp said:

Homework Statement


In the figure below the charge in the middle is
Q = -3.7 nC. For what charge
q1 will charge q2
be in static equilibrium?

Homework Equations


F = (K*q1*q2)/(r^2)

The Attempt at a Solution



I'm not sure where to go after acknowledging that Fq1->q = -Fq2->q
attachment.php?attachmentid=56732&d=1363310960.png



Let's see ...

q1 is twice the distance from q2 that Q is from q2, and we have an inverse square law.
 
  • #3
So that means the force is (3.7^2) = ~14 nC?
 
  • #4
rocapp said:
So that means the force is (3.7^2) = ~14 nC?
The unit for force is not Coulombs .

Why would you square the charge anyway ?
 
  • #5
I misunderstood the inverse square law.

F=q1=q2=k*q1*q2/r^2 = k*q1*Q/(r/2)^2

(9x10^9)*(q1*q2)/400 = (9x10^9)*q1*(3.7)/100

q1*q2/400 = q1*0.037
q2 = 14.8 N = F

Is that correct?
 
  • #6
rocapp said:
I misunderstood the inverse square law.

F=q1=q2=k*q1*q2/r^2 = k*q1*Q/(r/2)^2

(9x10^9)*(q1*q2)/400 = (9x10^9)*q1*(3.7)/100

q1*q2/400 = q1*0.037
q2 = 14.8 N = F

Is that correct?
Doubling distance reduces force to 1/4 , so to compensate for that, charge must be 4 times what is would be at Q . (Of course with opposite sign.)

So, is 14.8 = (4)(3.7) ?

... Yes. So you're O.K.
 
  • #7
Oh! Wow, that's a lot simpler than I was trying to make it. Thanks!
 

1. What is Coulomb's Law and how does it relate to electric charges?

Coulomb's Law is a fundamental principle in physics that describes the electrostatic interaction between two electrically charged particles. It states that the force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. In other words, the closer two charges are and the larger their magnitudes, the stronger the force between them will be.

2. How is Coulomb's Law used to calculate the force between two charges?

To calculate the force between two charges, we can use the formula F = k(q1q2)/r^2, where F is the force, k is the constant of proportionality (9 x 10^9 Nm^2/C^2), q1 and q2 are the magnitudes of the two charges, and r is the distance between them. This formula applies for both like and unlike charges.

3. What is the SI unit for electric charge?

The SI unit for electric charge is the Coulomb (C). One Coulomb is defined as the amount of charge that passes through a conductor in one second when the current is one ampere.

4. How does Coulomb's Law explain the concept of static equilibrium?

Coulomb's Law states that the force between two charges is directly proportional to their magnitudes. This means that if two charges of equal magnitude are placed at opposite ends of a system, their forces will cancel out and the system will be in static equilibrium. This concept is important in understanding the stability of atoms and molecules, as well as larger structures in the physical world.

5. What charge will make the two charges in static equilibrium?

If two charges of equal magnitude are placed at opposite ends of a system, the third charge that will make the system in static equilibrium will have the same magnitude as the other two, but with an opposite sign. This means that if the two existing charges are positive, the third charge should be negative, and vice versa. The distance between the charges will also play a role in determining the exact magnitude of the third charge.

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