I understand one approach to this homework problem. I don't understand why an alternative approach fails.
V = E*d
The Attempt at a Solution
The correct answer is (d), zero.
An acceptable approach:
1) Realize that V is the same at both corners
2) Thus, delta V = 0
3) delta U = q*V
4) If potential energy doesn't change, then no work has been done (or been "lost") from the system.
1) The particle experiences a rightwards force in the direction of the 2+ charge
2) To offset the right-wards pulling force and maintain a straight path, a new force, Fn, needs to be applied leftwards.
3) The force (Fn) is applied over a distance (Not the vertical distance between both charges. Instead: The horizontal distance that would otherwise exist were Fn not exerted)
4) This implies that energy has been exerted.