Question

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

Answer 1

electric field 7.64 10⁵ N / C

Step-by-step 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