Where can a third charge +Q be placed so that it experiences a zero force?

[shashaeee]

I'm having a hard time trying to picture the problem:

A charge of +2q is placed at the origin and a second charge of -q is placed at x= 3.0cm. Where can a third charge +Q be placed so that it experiences a zero force?

Here is how I picture the problem:

 

[berkeman]

I'm having a hard time trying to picture the problem:

A charge of +2q is placed at the origin and a second charge of -q is placed at x= 3.0cm. Where can a third charge +Q be placed so that it experiences a zero force?

Here is how I picture the problem:

View attachment 49498

The 3rd charge could end up anywhere on the line, left, right or between the first 2 charges. What is the equation for the electric field E generated by a charge at some distance...?

 

[shashaeee]

For Force its, F = KQQ/r²

The way I understand the problem is it could either be on the left or right of those two charges. Because if it was in the middle, the third charge will experience a net force directed to the right. Right?

 

[berkeman]

For Force its, F = KQQ/r²

The way I understand the problem is it could either be on the left or right of those two charges. Because if it was in the middle, the third charge will experience a net force directed to the right. Right?

Yes, that is correct. It's good that you see that.

 

[Nickie]

The first two charges are situated on the x-axis, with the +2q charge at the origin and the -q charge at x=3.0cm. In order for the third charge +Q to experience a zero force, it must be placed on the y-axis at a distance d from the origin. This distance can be calculated using Coulomb's Law, where the force between the two charges on the x-axis is equal to the force between the third charge and the +2q charge on the y-axis. This can be represented mathematically as F1 = F2, where F1 = (k * 2q * Q) / (3.0cm)^2 and F2 = (k * q * Q) / ((d)^2). Solving for d, we get d = 2.45cm. Therefore, the third charge +Q must be placed at a distance of 2.45cm on the y-axis from the origin in order to experience a zero force.