Electric Force and Charged Spheres

Soaring Crane

1. The problem statement, all variables and given/known data

Consider the following configuration of fixed, uniformly charged spheres on an xy coordinate system:
·a blue sphere fixed at the origin with positive charge q.
·a red sphere fixed at the point (d1,0) with unknown charge q_red,
·a yellow sphere fixed at the point (d2*cos theta, -d2*sin theta) with unknown charge q_yellow.

The net electric force on the blue sphere is observed to be vector F = (0,-F), where F>0 .

Here is a makeshift sketch:

O = charged particle

O_(q)___________O (d1, 0) q_red
--\
---\
----\O (d2*cos theta, -d2*sin theta) q_yellow

in which the dotted line between q at (0,0) and q_yellow is d2 and theta = angle between d2 and the x-axis (The x- axis is depicted by __________ pattern.)

What is the sign of the charge on the yellow sphere?
What is the sign of the charge on the red sphere?



2. Relevant equations

Possibly Coulomb’s Law:

F_mag = (k*|q1*q2|)/(r^2), where k = 8.988 * 10^9 N*m^2/C^2



3. The attempt at a solution

The y-component of the electric force is –F. The q_red particle does not have a y-component; it only has an x-component. The q_yellow charge has a y-component. If a – sign follows, then the q_yellow chage is positive since – indicates repulsion????


Is the q_red charge negative? If the electric force’s x-component is 0, then q_red’s x-component must be negative if q_yellow’s x-component is positive???

Thanks.