The electric field at point P due to a semi-infinite insulating rod can be determined by considering the contributions from different segments of the rod.

Let's break down the problem into smaller steps:

1. Electric Field Due to a Charged Rod:
The electric field at a point due to a charged rod can be calculated using the formula:
E = (k * λ) / r
where E is the electric field, k is the Coulomb's constant (9 x 10^9 N m^2/C^2), λ is the linear charge density, and r is the distance from the point to the rod. This formula gives the magnitude of the electric field.

2. Electric Field Due to an Infinitely Long Rod:
For an infinitely long rod, the electric field at a point P located at distance r from the rod is given by:
E = (k * λ) / r
This means that the electric field is inversely proportional to the distance from the rod. As the distance increases, the electric field decreases.

3. Electric Field Due to a Semi-Infinite Rod:
In the case of a semi-infinite rod, the electric field at point P can be determined by considering the contributions from two segments: the finite part (AB) and the semi-infinite part (BC).

- Electric Field Due to the Finite Part (AB):
The electric field at point P due to the finite part of the rod (AB) can be calculated using the formula mentioned earlier:
E_AB = (k * λ_AB) / r_AB
where λ_AB is the linear charge density of the finite part (AB) of the rod and r_AB is the distance from point P to the finite part (AB). Since the charge distribution is uniform along AB, λ_AB is equal to λ.

- Electric Field Due to the Semi-Infinite Part (BC):
The electric field at point P due to the semi-infinite part of the rod (BC) is zero. This is because the contribution from the infinite part of the rod cancels out due to the symmetry of the system.

Therefore, the total electric field at point P is given by the sum of the electric fields due to the finite part (AB) and the semi-infinite part (BC):
E_total = E_AB + E_BC = (k * λ) / r_AB

In conclusion, the electric field at point P due to a semi-infinite insulating rod with linear charge density λ is given by (k * λ) / r_AB, where k is Coulomb's constant and r_AB is the distance from point P to the finite part (AB) of the rod.