[KurzickMushroom]

Hi people! My question is:

2 charges, one of -10^-6 and the other of -3*10^-6 are .4 meters apart.

Where should a charge of -10^-7 be placed inorder that there be no resultant force on it?

Where should a charge of +10^-7 be placed in order that there be no resultant force on it?

I'm extremely confused over this...on the setup specifically. I think this is what the question wants to know:

kq1q2/(r)^2 + kq1q2/(r)^2 = 0

Each formula represents the force acting on the third sphere. Since the resultant force is = 0, both forces added up should equal to 0. Each way I set it up, the distance, r, gets cancelled out or gives me a negative answer.

Thanks in advance.

[Borek]

kq1q2/(r)^2 + kq1q2/(r)^2 = 0

Each formula represents the force acting on the third sphere.

Does it?

I assume q1 & q2 are two first charges. Where is the third charge? (It will cancel out in the end.)

Alternatively, you may solve looking for the place where electric field is zero.

[renge ishyo]

I remember this question, the thing that makes it hard is there is an implied second equation that you must use.

First I recommend drawing a picture. You need to do this to find out where you are placing the electron and the direction of the forces acting on it so that you write the correct equations (all three points should be in a straight line from what I remember). To do this for the first example where q₃ is -1 x10^-7C, you will notice that the charge has to be placed in between the two charges (q₁ and q₂) in order for the forces to balance. Now write the equation for the forces acting on q₃ from each of the other charges and set the two forces equal to each other.

Equation 1:

kq₁q₃/r₁₃² = kq₂q₃/r₂₃²

Notice that the distance to q₃ from each of the other charges is NOT the same. Therefore you will have two unknowns to solve for after you plug in your given values. These unknowns are r₁₃ and r₂₃. So you need another equation, and that equation is:

Equation 2:

r₁₃ + r₂₃ = .4m

You can solve this for either radius, such as :

r₁₃  = .4m - r₂₃

and plug the result into Equation 1. Now you have just one unknown left to solve for in equation 1, r₁₃. I solved this for the first example where q₃ = -1x10^-7C and I got that the distance from the -1x10^-6C charge was about .133 m and the distance from the -3x10^-6C charge was about .266 m. The setup for the second problem is similar with the twist being the change in the direction of the forces due to the positive charge (think about it while you are drawing your picture...you might not even have to calculate anything to solve part two...).

Hope this helped.

[KurzickMushroom]

thanks guys I'm getting something very close to your answer but still not exactly yet...probably a mathemical error since your method is quite sound. Thank you again for your time