Point charges and static equilibrium

In summary, the conversation discussed the concept of static equilibrium in a system of three point charges, where the net electric field is zero and the individual electric fields must add up to zero. The equation for static equilibrium was also mentioned, as well as the need to take distance into consideration. The question asked for the magnitude and sign of the third charge, which can be found by considering the distances between the three charges and solving for two simultaneous equations.
  • #1
elecstorm
3
0

Homework Statement



Two point charges q and 4q are distance L apart and free to move. A third charge is placed so that the entire three-charge system is in static equilibrium.

Homework Equations



[tex]\Sigma[/tex]F=0 This is the equation for static equilibrium
[tex]\vec{E}[/tex]=[tex]q/4\pi\epsilon_{0}r^2[/tex]

The Attempt at a Solution



If the three point charges are in static equilibrium, the net electric field is zero. So, [tex]\vec{E}[/tex]=0, which means that the individual electric fields of the point charges must add up to zero. Thus, the third charge must be -5q, as q + 4q = 5q.

Is any of this right?
 
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  • #2
No. There is a r^2 in the denominator. What happened to that? You have to take distance into consideration.
 
  • #3
Don't forget that the force on each of the three particles must be zero. Due to symmetries, and the fact that you need to find two quantities (charge and distance) you actually only need to consider any two particles, so that you get two simultaneous equations.
 
  • #4
Sorry, forgot to include the actual question. The question asks for the magnitude and sign of the third charge. I don't really understand the wording of this question. That is, should I assign another variable for the distance from the third charge? As well, is the magnitude of the third charge related to q, I don't think it is, because it does not ask for inclusion of the q variable in the answer...but I don't know how to calculate it otherwise. Thank you!
 
  • #5
Yes, take the dist of the 3rd charge from the 1st as x and then the dist q3-q2 will be L-x, if q3 is in between them.
 

FAQ: Point charges and static equilibrium

1. What is a point charge?

A point charge is a conceptual particle with a defined amount of electric charge, but no physical size or structure. It is often used in physics and engineering to simplify calculations involving electric fields and forces.

2. How is static equilibrium related to point charges?

Static equilibrium refers to a state in which an object is at rest or moving at a constant velocity, with all forces acting on it balanced. In the case of point charges, static equilibrium is achieved when the net force between them is zero, meaning they are at equal distances from each other and have opposite charges.

3. Can point charges have a non-zero net force on each other?

Yes, if the point charges have unequal magnitudes or are not in equilibrium, there will be a net force between them. This force will cause the charges to move towards or away from each other, depending on their charges.

4. How do you calculate the net force between two point charges?

The net force between two point charges can be calculated using Coulomb's law, which states that the force is directly proportional to the product of the two charges and inversely proportional to the distance between them squared. The formula is F = (k * q1 * q2) / r^2, where k is the Coulomb's constant, q1 and q2 are the charges, and r is the distance between them.

5. What is the unit of electric charge for point charges?

The unit of electric charge for point charges is the Coulomb (C). It is defined as the amount of charge that passes through a point in a conductor in one second when there is a constant current of one ampere.

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