In this scenario, two infinite identical charged sheets and a charged spherical body with charge density ' $\rho$ ' are positioned as shown in the figure. We aim to determine the relationship between the electrical fields at points A, B, C, and D.

When considering the electric fields:

Electric Field Due to Charged Sheets:

The infinite charged sheets produce a uniform electric field. The electric field due to a single infinite sheet of charge is constant on either side of the sheet and is directed perpendicularly away from the sheet.

Electric Field Due to a Spherical Charge:

Outside the charged sphere, the electric field behaves as if the entire charge were concentrated at the center of the sphere. The electric field decreases with the square of the distance from the center, following the inverse square law.

Given these principles:

At Points C and D: These are located in different regions regarding the charged sheets and spherical body. Due to the inverse square nature of the electric field from the spherical charge and the uniform field of the sheets, the field strength will vary, resulting in $\vec{E}_C \neq \vec{E}_D$.

At Points A and B: Both points are influenced by the uniform field of the charged sheets. However, if the distance or position concerning the sphere also affects these points, this could lead to differences in field strength, thus $\vec{E}_A > \vec{E}_B$.

This analysis leads us to conclude that the electric field relations are $\mathrm{E}_{\mathrm{C}} \neq \mathrm{E}_{\mathrm{D}}$ and $\mathrm{E}_{\mathrm{A}} > \mathrm{E}_{\mathrm{B}}$.