In electrostatic conditions, no electric field can exist inside a conductor.
As the distance r=5 cm falls inside the conductor, the electric field is just zero.
b)
Same as above, as r=10 cm is still inside the spherical conductor.
c)
At r= 50 cm. from the center of the spherical conductor, we can apply Gauss' Law in order to get the value of the electric field.
By symmetry, the electric field, at a same distance from the center, must be radial, and constant on a spherical surface concentric with the spherical conductor.
So, we can write the following equation for Gauss'Law:
If E is constant, we can take it out of the integral, and integrate all the closed spherical surface, as follows:
So, we can solve for E, as follows:
E = -9*10⁵ N/C (radially inward, taking the outward direction as positive)