Suppose you want to find the field of the charge q relative to the coorinate system on the picture. That wont be very hard to do and the field will in general have both a vertical and horizontal component. Now suppose we let the charge get very very far out on the x-axis, such that the horizontal distance to the origin is much much larger than the vertical distance from the origin to q. My question is: Will the vertical component of the force then be negligible compared to the horizontal? Because geometry does seem to suggest that, but on the other hand it is not really intuitive to me why. Evidently it is not like you are moving further away vertically than horizontally, it's rather the opposite.