Electric Fields - Net Charge on Point Charges

In summary: Let's try the one that depends on q but not r: \frac{kq_1 q_2}{r_{12}^2} + \frac{kq_1 q_3}{r_{13}^2} =0
  • #1
dh743
15
0

Homework Statement


Two point charges are placed on the x axis: +5 microC charge at x=0 and +8 microC charge at x=0.9m. Where on the x-axis can a third charge be placed so that the net charge on all three charges is zero? Determine the magnitude of the third charge.


Homework Equations


E=[tex]\frac{kQq}{r2}[/tex]


The Attempt at a Solution


It's difficult to type on here but basically I let E of the two given charges equal each other to find a point but I have no idea how to complete the rest of the question. The given answer is a charge of -1.56[tex]\mu[/tex]C at x=0.397m.

Thank you
 
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  • #2
Having the "net charge on all three charges is zero" doesn't sound right. Are you sure they aren't asking that the net force on each charge be zero? If I answer that question, I get the answers that you claim. Also, what you're calling E is really the force between the charges q and Q.
 
  • #3
fzero said:
Having the "net charge on all three charges is zero" doesn't sound right. Are you sure they aren't asking that the net force on each charge be zero? If I answer that question, I get the answers that you claim. Also, what you're calling E is really the force between the charges q and Q.
Yeah you're right, it does mean the net force on each charge is zero. How did you get the answer though?
 
  • #4
Place a charge q at x=r and compute the net force on each charge. By setting these equal to zero, you have a system of equations that can be solved for q and r.
 
  • #5
fzero said:
Place a charge q at x=r and compute the net force on each charge. By setting these equal to zero, you have a system of equations that can be solved for q and r.
That makes sense, but how do I now arrange it to avoid having 2 unknowns?
 
  • #6
dh743 said:
That makes sense, but how do I now arrange it to avoid having 2 unknowns?

You should have 3 equations in all, pick any 2 of them to solve. Post your results if you're having trouble.
 
  • #7
fzero said:
You should have 3 equations in all, pick any 2 of them to solve. Post your results if you're having trouble.
Ok letting 5 microC be y and 8 microC be z, this is I've ended up with:
Ey=[tex]\frac{kq}{r2}[/tex]
Ez=[tex]\frac{kq}{(0.9-r)2}[/tex]
Eq = [tex]\frac{k(5microC}{r2}[/tex] + [tex]\frac{k(8 microC}{(0.9-r)2}[/tex]

I can't solve them because I always end up with 2 unknowns so I must have made a mistake somewhere.
 
  • #8
You need to compute the forces, not just electric fields. Draw a force diagram for each charge if you need to. Charge 1 experiences a force from charge 2 and another from charge 3, and you'll get an equation that looks like

[tex] \frac{kq_1 q_2}{r_{12}^2} + \frac{kq_1 q_3}{r_{13}^2} =0,[/tex]

with similar equations for the other charges.
 
  • #9
Thanks for all your help, but I still can't get it to a point where I only have one unknown - I always end up with both q and r as unknowns. And what do the subscript 12 and 13 mean in your above equation?
 
  • #10
dh743 said:
Thanks for all your help, but I still can't get it to a point where I only have one unknown - I always end up with both q and r as unknowns. And what do the subscript 12 and 13 mean in your above equation?

[tex]r_{12}[/tex] is the distance between charge 1 and charge 2, etc. As for solving for q and r, you have 3 equations to pick from. One equation depends on r but not q, so we can use that to solve for r. Either of the other two equations can then be used to solve for q.
 

1. What is an electric field?

An electric field is a physical field that is created by electrically charged objects. It is a fundamental concept in the study of electricity and is represented by a vector quantity that describes the direction and strength of the force that a charged particle would experience at any point in space.

2. How is an electric field created?

An electric field is created when a charged object, such as an electron or a proton, is placed in a space. The charged object exerts a force on other charged particles in the space, creating an electric field. The strength of the electric field is dependent on the magnitude of the charges and the distance between them.

3. What is net charge?

Net charge is the total amount of electric charge on an object or system. It is determined by adding up the charges of all the individual particles within the object. An object with a net charge will create an electric field around it.

4. How does the net charge affect the electric field?

The net charge of an object determines the strength of the electric field it creates. The greater the net charge, the stronger the electric field. Additionally, objects with opposite net charges will create an electric field that pulls them towards each other, while objects with like net charges will create an electric field that pushes them away from each other.

5. Can the net charge on a point charge be zero?

Yes, the net charge on a point charge can be zero if the charge of the particles within the object cancel each other out. This is known as a neutral point charge and it will not create an electric field.

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