Answer:
(a) 
(b) 
(c) 
Explanation:
(a)
Given:
Charge on sphere (Q) = 
Radius of sphere (R) = 11.0 cm = 0.110 m
Distance from the center (r) = 5 cm = 0.05 m
Coulomb's constant (k) = 
Now, we know from Gaussian law for uniform charged spheres, the electric field at a distance 'r ≤ R' from the center of sphere is given as:

Plug in the given values and solve for 'E'. This gives,

(b)
Given:
Charge on sphere (Q) = 
Radius of sphere (R) = 11.0 cm = 0.110 m
Distance from the center (r) = 10 cm = 0.10 m
Now, we know from Gaussian law for uniform charged spheres, the electric field at a distance 'r ≤ R' from the center of sphere is given as:

Plug in the given values and solve for 'E'. This gives,

(c)
Given:
Charge on sphere (Q) = 
Radius of sphere (R) = 11.0 cm = 0.110 m
Distance from the center (r) = 50 cm = 0.50 m
Now, we know from Gaussian law for uniform charged spheres, the electric field at a distance 'r > R' from the center of sphere is given as:

Plug in the given values and solve for 'E'. This gives,
