Find Charges for Red and Yellow Sphere at Origin

[StephenDoty]

blue sphere is fixed at the origin with positive charge q,
a red sphere fixed at the point (d_1,\,0) with unknown charge q_red, and
a yellow sphere fixed at the point (d_2\cos(\theta),-d_2\sin(\theta)) with unknown charge q_yellow.

The net electric force on the blue sphere has a magnitude F and is directed in the - y direction.

Is the charge for the red sphere positive or negative? Is the charge for the yellow sphere positive or negative?


Since the blue sphere is positive and the net force is in the -y direction wouldn't the red sphere be positive, making the force on the blue sphere by the red sphere to the left and the yellow sphere be negative making the force go down and to the right, and since the yellow sphere is closer its force magnitude on the blue sphere would be bigger than that of the red sphere making the net force point in the -y direction?

 

[tiny-tim]

Hi Stephen!

Since the blue sphere is positive and the net force is in the -y direction wouldn't the red sphere be positive, making the force on the blue sphere by the red sphere to the left and the yellow sphere be negative making the force go down and to the right,

That's right!

and since the yellow sphere is closer its force magnitude on the blue sphere would be bigger than that of the red sphere making the net force point in the -y direction?

But we don't know the relative size of d_1 and d_2 …

or is there something you're not telling us?

 

[StephenDoty]

I regurgitated all of the information I was given on the problem. The size of the charges would have made this problem much easier.

So would the red sphere be positive and the yellow sphere be negative?

 

[tiny-tim]

I regurgitated all of the information I was given on the problem. The size of the charges would have made this problem much easier.

So would the red sphere be positive and the yellow sphere be negative?

Yes!

(i already said that … )

hmm … I can see the picture at last …

yes, the yellow sphere certainly does look closer …

and since the yellow sphere is closer its force magnitude on the blue sphere would be bigger than that of the red sphere making the net force point in the -y direction?

you don't need this … the question doesn't ask for it …

you've already given a fully satisfactory answer …

and the yellow force might be bigger because the yellow charge is bigger …