Point of Equilibrium between two charges

In summary: So case a is when the q force is greater than the -q force and case b is when the -q force is greater than the q force.Right! So case a is when the q force is greater than the -q force and case b is when the -q force is greater than the q force.In summary,The homework statement asks for help understanding how the forces of attraction between opposite charges affect the equilibrium of an electron. In order to find the equilibrium, it is necessary to know the distance between the charges, the relative size of the forces, and the scenarios in which the equilibrium is possible.
  • #1
jegues
1,097
3

Homework Statement



See figure attached for problem statement.

Homework Equations





The Attempt at a Solution



I'm a little confused on how to start on this one.

Okay so I know that the two particles with oppsite charge attract one another, and a 3q force of attraction is going to be larger than a -q force of attraction.(and vice versa)

So is it in cases (c) and (d) that an electron will find its point of equilibrium to the left of the particles?
 

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  • #2
jegues said:
and a 3q force of attraction is going to be larger than a -q force of attraction.(and vice versa)
Not always. What else does the force of attraction depend on?
 
  • #3
Doc Al said:
Not always. What else does the force of attraction depend on?

The distance between the two charges?
 
  • #4
jegues said:
The distance between the two charges?
Yes. Now combine those two factors to see which arrangements can meet the criteria.
 
  • #5
Doc Al said:
Yes. Now combine those two factors to see which arrangements can meet the criteria.

I'm still not seeing how to do that. Can you give me another nudge?

EDIT: The forces on each other should be 0 in equilibrium so we're looking at the following,

[tex]F = k \frac{1*3}{r^{2}}[/tex]

Now in some scenarios,

[tex]\vec{F_{ab}} = k \frac{1*3}{r^{2}} \hat{i}[/tex]

and in others

[tex]\vec{F_{ab}} = - k \frac{1*3}{r^{2}} \hat{i}[/tex]
 
  • #6
jegues said:
I'm still not seeing how to do that. Can you give me another nudge?
Sure. In order for the net force on the electron to be zero, what must be the relative size of F_1 and F_2? In which configurations is that not possible?
 
  • #7
Doc Al said:
Sure. In order for the net force on the electron to be zero, what must be the relative size of F_1 and F_2? In which configurations is that not possible?

Are we to assume that the electron has a charge of -1q?

How do we know what force and electron will have on the given particles?
 
  • #8
jegues said:
Are we to assume that the electron has a charge of -1q?
That doesn't matter. (But you can assume that if you like.)

How do we know what force and electron will have on the given particles?
All we care about is the net force on the electron. Compare the force on the electron from each of the two charges. Hint: In some cases the force from one charge will always be greater than the force from the other, for an electron placed to the left.
 
  • #9
Doc Al said:
That doesn't matter. (But you can assume that if you like.)


All we care about is the net force on the electron. Compare the force on the electron from each of the two charges. Hint: In some cases the force from one charge will always be greater than the force from the other, for an electron placed to the left.

Ah I see it now, it can only be done in cases a and b!
 
  • #10
jegues said:
Ah I see it now, it can only be done in cases a and b!
Right!
 

Related to Point of Equilibrium between two charges

1. What is the Point of Equilibrium between two charges?

The Point of Equilibrium between two charges, also known as the electric potential, is the point where the net force on a small positive test charge is zero. At this point, the electric potential energy of the test charge is at its lowest and it remains stable.

2. How is the Point of Equilibrium between two charges calculated?

The Point of Equilibrium can be calculated using Coulomb's Law, which states that the electric force between two charges is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them.

3. Is the Point of Equilibrium between two charges always in the middle?

No, the Point of Equilibrium can be anywhere between the two charges, depending on the magnitude and distance between them. If the two charges are of equal magnitude, the Point of Equilibrium will be in the middle. However, if one charge is larger than the other, the Point of Equilibrium will be closer to the larger charge.

4. How does the Point of Equilibrium between two charges affect the electric field?

The Point of Equilibrium is the point where the electric field is zero. This means that the electric field lines are evenly distributed around the two charges, with equal strength and in opposite directions.

5. Can the Point of Equilibrium change?

Yes, the Point of Equilibrium can change if the magnitude or distance of the two charges changes. It can also be affected by the presence of other charges in the surrounding area, as they can alter the electric field and the Point of Equilibrium.

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