Final answer:
The electric field due to a hemispherical shell along the z-axis at a point on the z-axis is directed along the positive z-axis, as a consequence of symmetry in spherically symmetrical situations. Option D is correct.
Step-by-step explanation:
The electric field due to a hemispherical shell along the z-axis at a point on the z-axis is directed along the positive z-axis. This conclusion is based on the consequences of symmetry for the electric field in a spherically symmetrical situation.
According to Essential Knowledge 2.C.3, for a spherically symmetric charged object, the electric field is radial and its magnitude varies as the inverse square of the radial distance from the center of the object.
Furthermore, due to the symmetry of the charge distribution on the hemisphere, the horizontal (x- and y-) components of the electric field cancel out, leaving only the vertical z-component.
In other words, the electric field is only dependent on the z-coordinate and points either away from the plane of symmetry in the case of positive charge density or toward it in case of negative charge density, along the z-axis.