Electric Potential Energy and Sign

[always_tired]

There is a negative point charge with a positively charged plate above it and a negatively charged plate below it. Define up as positive and down as negative. When the point charge moves towards the positively charged plate it does negative work. Why? The force the charge experiences is upward in the positive direction and it moves in the same direction as the force.

 

[BvU]

It loses potential energy. That can be used to pull up something that is pulling downwards.

Just like a mass does when it goes from a high position to a lower position.

 

[always_tired]

? It gains potential energy.

 

[haruspex]

? It gains potential energy.

It gains gravitational PE but loses (more) electrostatic PE.

 

[always_tired]

No, it gains electrostatic potential energy. deltaU = -W; work is negative in this case; potential energy increases. From "University Physics" by Young and Freedman:

"Negative charge moves in the direction of the electric field, field does negative work, potential energy increases" (pg 756)

I'm wondering why this is true.

 

[haruspex]

"Negative charge moves in the direction of the electric field, field does negative work, potential energy increases" (pg 756)

I can only suppose that should say "If the negative charge ..."
In the OP, the direction of the field is down and the charge is moving up, so against the field. Correspondingly, the field is doing positive work and the electrostatic PE decreases.

 

[BvU]

"Negative charge moves in the direction of the electric field, field does negative work, potential energy increases" (pg 756)

I'm wondering why this is true.

Perhaps $\Delta {\rm potential\ energy} = q\Delta V$ ?

In your description the negative charge moves against the direction of the electric field !And what helped me was to draw a few graphs for a fixed single positive point charge case: 1/r² for E, 1/r for V. And move a positive test charge from A to B >A. Then idem negative test charge.

I liked this presentation.