ElectroStatic Equilibrium problem

[RandellK02]

Homework Statement

particle 1 of charge q1 (at origin) and particle 2 of charge q2 = 3q1, are held at separation L on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a) x and (b) y coordinates of particle 3?

Homework Equations

F=k|q1||q2|/d²

The Attempt at a Solution

I assumed q1 and q2 are like charges so I put q3 in the middle. This could be my mistake since I am getting incorrect answers for x, I do know y = 0.
If q3 does belong between the two charges on the X axis, then I am not setting up my d² part of Coulombs law. Could someone point me to the right direction?
Net Force = 0
F₃₁=k|q3||q1|/?²
F₃₂=k|q3||q2|/?²

 

[wukunlin]

if the particle is at distance d away from q1, what distance is it between the particle and q2? assuming this is a one dimensional problem

 

[RandellK02]

if the particle is at distance d away from q1, what distance is it between the particle and q2? assuming this is a one dimensional problem

Okay say, if distance between q3 and q2 =d than distance between q3 and q1 is L - d correct? So...
kq₃q₁/(L-d)²=kq₃q₂/d²
=>q₁/(L-d)²=q₂/d²

If the above steps are correct... is it safe to assume to use the fact: q₂=3q₁ to eliminate the two charges?

 

[wukunlin]

yes :)

 

[rwisz]

As a scientist, it is important to carefully analyze the given information and equations in order to provide an accurate response. In this scenario, we have three particles with known charges and a separation distance between them. Our goal is to determine the coordinates of the third particle, q3, in order to achieve electrostatic equilibrium.

First, we need to understand the concept of electrostatic equilibrium. In simple terms, it means that the net electrostatic force on a particle is equal to zero. This can be achieved by placing the third particle at a specific location where the forces from the other two particles cancel each other out.

In order to find the coordinates of q3, we can use Coulomb's law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Therefore, the net force on q3 can be expressed as:

Fnet = F31 + F32 = k|q1||q3|/d12 + k|q2||q3|/d22

Since we want the net force to be zero, we can set this equation equal to zero and solve for d1 and d2, the distances between q1 and q3, and q2 and q3, respectively. This will give us the coordinates of q3 along the x-axis.

We can also use trigonometry to determine the y-coordinate of q3. Since the net force on q3 is zero, the forces from q1 and q2 must be equal in magnitude and opposite in direction. This means that the angle between the x-axis and the line connecting q3 and q1 must be the same as the angle between the x-axis and the line connecting q3 and q2. By using this information, we can set up a right triangle and use trigonometric functions to solve for the y-coordinate of q3.

In conclusion, by carefully analyzing the given information and using Coulomb's law and trigonometry, we can determine the coordinates of q3 in order to achieve electrostatic equilibrium. It is important to note that the assumption that q1 and q2 are like charges may not always be correct, and the solution may be different in that case. Therefore, it is important to carefully consider all possible scenarios and use the appropriate equations to provide an accurate response.