Why Is My Calculation of Electrostatic Equilibrium Incorrect?

[cs44167]

Homework Statement

A charge of 2.0 microcoulombs is positioned at (0,0) and a charge of -6.0 microcoulombs is positioned at (3,0). Where must a third charge be placed in order to be in electrostatic equilibrium?

Relevant Equations

Electrostatic Force = kq1q2/d^2

I set the electrostatic force exerted by the object at (0,0) and (3,0) equal to each other, dividing out k and q2. I was left with q1/d^2 for both terms and substituted in the given charges for each object. I then replaced d^2 for the object at (0,0) with “x^2” and d^2 for the object at (3,0) with “(3-x)^2”. I got an answer of (1.098, 0) which made sense that it would be somewhere left of 1.50, but was incorrect.

Any helpers in where I went wrong? Thanks.

 

[Orodruin]

In which directions do the forces go?

 

[cs44167]

In which directions do the forces go?

So the third charge would have to be to the left of the origin, correct?

Then you would have negative-positive-negative.

From there I’m struggling with Coulomb’s Law because we don’t know the magnitude of the charge on the third object. I have q3q1/x^2 =q1q2/3^2 but we don’t know x or q3.

 

[etotheipi]

So the third charge would have to be to the left of the origin, correct?

Then you would have negative-positive-negative.

From there I’m struggling with Coulomb’s Law because we don’t know the magnitude of the charge on the third object. I have q3q1/x^2 =q1q2/3^2 but we don’t know x or q3.

Make sure to draw a diagram. Try positioning this third charge at a distance $d$ to the left of the origin, and then draw on the forces. I don't believe you need to know $q_{3}$.

 

[PeroK]

So the third charge would have to be to the left of the origin, correct?

Then you would have negative-positive-negative.

From there I’m struggling with Coulomb’s Law because we don’t know the magnitude of the charge on the third object. I have q3q1/x^2 =q1q2/3^2 but we don’t know x or q3.

You can look at this two ways. You can take any charge $q_3$ and try to make the total force on $q_3$ due to $q_1$ and $q_2$ equal to zero. If $q_3$ doesn't cancel out, then you have a serious conceptual or mathematical problem!

Or, you can look for a position where the electric field due to $q_1$ and $q_2$ is zero. Then, clearly, the value of $q_3$ is irrelevant.

 

[jbriggs444]

I have q3q1/x^2 =q1q2/3^2 but we don’t know x or q3.

Can you write down in words what $\frac{q_3q_1}{x^2}$ is supposed to be? It is the force of object [which] on object [which other]?

Can you write down in words what $\frac{q_3q_2}{3^2}$ is supposed to be? It is the force of object [which] on object [which other]?

Which object are you trying to find the force on?