Final answer:
The electric field of a point charge at the origin must point radially in the direction from the origin to any point in space because of spherical symmetry.
Step-by-step explanation:
Due to symmetry, the electric field of a point charge at the origin must point in a specific direction. In spherically symmetric cases, such as a point charge at the origin, the electric field at any point must be radially directed. This is because the electric field is determined by the charge distribution, and a point charge at the origin has a symmetrical charge distribution in all directions from the point.
Therefore, the electric field at any point P located at a distance r from the center will be represented using spherical coordinates as Ép = Ep(r)î, where î is the unit vector pointed in the direction from the origin to the field point P. The radial component Ep can be positive or negative: if Ep > 0, the electric field at P points away from the origin (towards positive charges), and if Ep < 0, the electric field at P points toward the origin (towards negative charges).