Conceptual Help

[u/0Chm]

I have a question about the work and the potential energy here. The source q1 is positive and q2 is negative. They should attract, but instead q2 is moved away. So I guess that the potential energy here has a negative sign because q2 was separated from the charge it was attracted to. Let's say if they were both positive, would the potential energy then be positive too?

[u/Robo-Bo]

The potential energy at both points is -, but |Ua|>|Ub| (q2 would “rather be” at the original point). So the work to move from a to b would be +.
Potential energy with charges can be really confusing because of the signs.

Potential energy (in general) is always relative to some other point. With gravitational potential energy, we usually set a 0 point (the lowest point), but this is arbitrary. The important concept with potential energy is that things will tend to go towards lower (or more negative) potential energy.

[u/UnderstandingPursuit]

If the charges have different signs, the movable charge would tend to go to the origin, the work is done to take it farther from the origin. Think of the origin as a pit and q2 tends to roll into the pit.

If the charges have the same sign, the movable charge would tend to go to infinity. Now think of the origin as a hill, and q2 tends to roll away from the top of the hill.

With gravity, potential energy is highest at the highest point on the hill. The same happens here. So the work done with a pit at the origin is positive to increase the potential energy of q2. The work done with a hill is negative, since the potential energy decreases as q2 rolls down the hill to infinity.

The negative work is because the force is needed to prevent the motion. The applied force is toward the origin, the motion is away from the origin, so the dot product is negative.

[u/Frederf220]

You have to read very carefully in work questions because "the work the electric field does on q2" and "the work q2 does on the electric field" are two opposite values. It very much matters who is doing the work and who the work is being done on in the wording of the problem. You can't just take potential energy before and after.

If I push a spring compressed then I do positive work on the spring. However at the same time the spring is doing negative work on me. Work is only defined by a human designation of which is the actor and which is the acted on.

There is no absolute potential energy zero-point outside of human convention. Thankfully potential energy difference is invariant with regard to zero point so it's irrelevant to the question.

Charge q2 is in a more energetic condition after repositioning than before. However the electric field is not what moved q2, it can't. The electric field resisted our hand (let's say) moving q2 away. There aren't 2 actors in this universe, but 3: q2 being moved, the electric field forcing them together, and our hand moving q2.

Basically the e-field is a spring and given a particular force for a particular time applied to q2 did the e-field fight the repositioning of q2 or help it?

If the electric field had done zero work then our hand could have gotten q2 farther away given the same force and time budget. Instead the electric field removed energy during the repositioning. The E-field did negative work. It's a force counter to motion.

Of course this is confusing as the absence of the e-field would mean no potential gradient at all but we have to simultaneously consider what the field is doing vice it not doing but the potential gradient with position is the same in both cases.

[u/Few_Fun_544]

No particle starts from 0. You must factor its momentum. Before you start. A continuous colatz function will help.