Two small insulating spheres with radius 9.00*10^-2m are separated by a large center-to-center distance of 0.520m . one sphere is negatively charged, with net charge -2.40uc , and the other sphere is positively charged, with net charge 3.35uc . the charge is uniformly distributed within the volume of each sphere.
a)what is the magnitude e of the electric field midway between the spheres?
take the permittivity of free space to be ? 0 = 8.85

electric field  7.64 10⁵ N / C

Explanation:

For this problem we can use Gauss's law, which indicates that the load within a Gaussian surface can be considered located in its center, therefore, as the point is much greater than the radius of the spheres we can take them as if it were a spot loading Let's calculate the field at the midpoint between them

            r = 0.520 m / 2

            r = 0.260 m

The electric field is a vector

            Et = E1 + E2

E1 has a negative charge, so the force is attractive and E2 has a positive charge, the outside is repulsive, so the two forces point in the same direction on the positive test charge.

               E1 = k Q1 / r²

               E2 = k Q2 / r²

               Et = E1 + E2

               Et = k Q1 / r² + k Q2 / r² = k (Q1 + Q2) / r²

               Et = 8.99 10⁹ (2.4 10⁻⁶ + 3.35 10⁻⁶) / 0.26²

               Et = 7.64 10⁵ N / C