Where on the x-axis will a third charge have no net force

[bbraves7]

Homework Statement

Where on the x-axis would the net force on a (-2) micro Coulomb charge be zero?

*picture attached*

Homework Equations

F = k*(q1q2)/d^2

The Attempt at a Solution

I think the answer is d= 6, making the position on the x-axis = 7. However, when solving my equation, I have to take the square root of a negative number, which obviously has no real answer. I couldn't seem to logic my way around it, so what am I missing? Other than expressing the answer in terms of i, how can I get around this??

 

[SammyS]

9 μC = 9×10^‒6 C , Similarly ‒4 μC = ‒4×10^‒6 C and ‒2 μC = ‒2×10^‒6 C.

You have written them as 9^‒6 C, ‒4^‒6 C, and ‒2^‒6 C .

(Maybe you are simply using a non-standard notation.)

 

[SammyS]

You need F₁ + F₂ = 0.

So that F₁ = ‒ F₂

That should take care of your signs.

 

[bbraves7]

9 μC = 9×10^‒6 C , Similarly ‒4 μC = ‒4×10^‒6 C and ‒2 μC = ‒2×10^‒6 C.

You have written them as 9^‒6 C, ‒4^‒6 C, and ‒2^‒6 C .

(Maybe you are simply using a non-standard notation.)

Yeah, I just write it like that as a kind of short hand.

Anyways, I figured out what I was doing wrong. The equation should only be used to calculate the magnitude of the force, so I shouldn't put the negative in the equation for the -4 micro Coulomb charge. That takes care of it. Thanks for the reply though.

 

[rwisz]

Your logic is correct. The net force on the charge would be zero when it is located at a distance of 6 units from the -1 micro Coulomb charge, making its position on the x-axis 7 units. However, when solving for the distance using the equation F = k*(q1q2)/d^2, you should not be taking the square root of a negative number. The equation should be set up as follows:

F = k*(q1q2)/d^2
0 = k*(-1 micro C)(-2 micro C)/(d-7)^2
0 = (9x10^9)(2x10^-12)/(d-7)^2
0 = (1.8x10^-2)/(d-7)^2

Solving for d, we get d = 7, which is the correct answer. There is no need to take the square root of a negative number in this case. If you are getting a negative number when solving for d, it is likely that you made a calculation error. Double check your calculations to ensure that you are getting the correct answer.