I know this question's been asked extensively on the site. I've read a couple answers here and there, but none of them satisfy my curiosity and confusion.
Here's what I do understand:
an electric field is an alteration of space caused by a charge
the alteration of space is the agent that produces a force on nearby charges
Here's my confusion:
Suppose we have a negative source charge and a negative probe charge. We know the two will repel each other, so the force vector for the probe charge points outward, away from the source charge.
My textbook says that if the probe charge is negative (which it is in this case), the electric field vector points in a direction opposite to that of the force vector.
This suggests that the electric field vector points inward towards to the negative source charge, whereas the force vector on the probe charge points outward away from the source charge.
But if the electric field is what generates the force on the probe charge, how exactly is it possible for the inward-pointing electric field to push the probe charge in the opposite direction?