One final problem involving electrical fields

[avb203796]

A sphere with a charge of 5.0 x 10^-6 C is placed one fifth of the distance between two negatively charged spheres, as measured from the left. The sphere to the left has a charge of -3.0 x 10^-6 C and the sphere to the right has a charge of -6.0 x 10^-6 C. A distance of 10.0cm separates the end spheres. Calculate the net force on the positively charged sphere. In what direction is the net force? What is the net electric field that the positively charged sphere experiences? Is there a point where the net electrical field is zero? If so, where?

Ok so I am not positive how to go about solving this one. I know that teo point charges separated by given distance exert the same force on each other therefore I would think that there is a point where the net electrical field is zero and I would guess that point would be at 5.0 cm but i am not sure. where do I go from here?

 

[Astronuc]

How about treating the spheres as point charges? Then the location is given by the location of the center of the spheres.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefor.html#c2

Then try starting with writing the equation for the Coulomb electric force. There is one equation for the left (-) sphere and (+) sphere, and there is a second equation for the right (-) sphere and (+) sphere.

Since the (+) sphere is one-fifth the way between, one distance is 0.2 the separation of the two negative spheres and the other distance is 0.8 the separation.

The negatively charged spheres have different magnitudes of negative charge, so the zero electric is not midway.

 

[avb203796]

So then after I get the two forces do I just add them to get the net force? And after I have the net force how do I go about the rest of the problem?