Final answer:
The charge distributed uniformly over the volume of an insulating sphere with a radius of 5.00 cm is 19.08 * 10^6 C/m^3.
Step-by-step explanation:
In order to find the charge distributed uniformly over the volume of an insulating sphere, we need to use the formula:
Charge = Volume * Charge density
The volume of a sphere is given by the formula:
Volume = (4/3) * pi * r^3
Substituting the given radius of 5.00 cm (0.05 m) into the formula, we get:
Volume = (4/3) * pi * (0.05 m)^3 = 5.24 x 10^-4 m^3
The charge density is the total charge divided by the volume. Since the charge is distributed uniformly, the total charge is equal to the charge density times the volume:
Total charge = Charge density * Volume
Substituting the given total charge of 10.00 μC into the formula, we get:
10.00 μC = Charge density * 5.24 x 10^-4 m^3
Solving for the charge density, we find:
Charge density = 10.00 μC / 5.24 x 10^-4 m^3 = 19.08 * 10^6 C/m^3
Therefore, the charge distributed uniformly over the volume of the insulating sphere is 19.08 * 10^6 C/m^3.