Electric Fields - Net Charge on Point Charges

[dh743]

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=$$\frac{kQq}{r²}$$

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$$\mu$$C at x=0.397m.

Thank you

 

[fzero]

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.

 

[dh743]

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?

 

[fzero]

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.

 

[dh743]

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?

 

[fzero]

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.

 

[dh743]

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=$$\frac{kq}{r²}$$
Ez=$$\frac{kq}{(0.9-r)²}$$
Eq = $$\frac{k(5microC}{r²}$$ + $$\frac{k(8 microC}{(0.9-r)²}$$

I can't solve them because I always end up with 2 unknowns so I must have made a mistake somewhere.

 

[fzero]

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

$$\frac{kq_1 q_2}{r_{12}^2} + \frac{kq_1 q_3}{r_{13}^2} =0,$$

with similar equations for the other charges.

 

[dh743]

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?

 

[fzero]

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?

$$r_{12}$$ 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.