Answer:
(a). If z = 0, The electric field due to the rod is zero.
(b). If z = ∞, The electric field due to the rod is
.
(c). The positive distance is 
(d). The maximum magnitude of electric field is 
Explanation:
Given that,
Radius = 2.00 cm
Charge = 4.00 mC
(a). If the radius and charge are R and Q.
We need to calculate the electric field due to the rod
Using formula of electric field

Where, Q = charge
z = distance
If z = 0,
Then, The electric field is

(b). If z = ∞, z>>R
So, R = 0
Then, the electric field is


(c). In terms of R,
We need to calculate the positive distance
If 
Then, 

Taking only positive distance

(d). If R = 2.00 and Q = 4.00 mC
We need to calculate the maximum magnitude of electric field
Using formula of electric field




Hence, (a). If z = 0, The electric field due to the rod is zero.
(b). If z = ∞, The electric field due to the rod is
.
(c). The positive distance is 
(d). The maximum magnitude of electric field is 