Two small insulating spheres with radius 9.00×10−2m are separated by a large center-to-center distance of 0.545 m . One sphere is negatively charged, with net charge -2.35 μC , and the other sphere is positively charged, with net charge 4.35 μC . The charge is uniformly distributed within the volume of each sphere.
What is the charge at the midway point between charged spheres
Gauss' Law: I will use ∫ for closed surface integral
The Attempt at a Solution
I used two gaussian surfaces. One encapsulating the negatively charged sphere and one the positively charged sphere. The radius of my gaussian surface was half the distance between the spheres, 0.2725m.
In gauss' law E can come out of the integral and the integral of dA is A.
Area of sphere is 4πr2
This E will be pointing away from the negatively charged sphere at the midpoint between two charged spheres.
I did this for the positively charged sphere as well using a gaussian surface with the same radius(as above). I obtained an Electric field that this sphere contributes at the midpoint. I summed them up and got a total electric field. This answer is incorrect.
Not sure what I am doing wrong,
The problem gives the radius of both charged spheres so maybe this comes into play somewhere?
Thanks a bunch!