Sign of potential energy for opposite charges at fixed distance

[pat666]

Homework Statement

Two charges, one positive and one negative, are separated by a fixed distance.
The sign of the potential energy of this pair
is always positive;
is always negative;
is sometimes positive and sometimes negative;
depends on the distance.

Homework Equations

The Attempt at a Solution

I think that it is sometimes positive and sometimes negative; since it would depend on the magnitude of the individual charges?

 

[graphene]

what is the expression for potential energy of two charges?

 

[Pythagorean]

No superposition requred here. Potential energy is a property of the two particle system. A single particle would have none.

 

[pat666]

apparently not then- can something have negative potential energy? I am now thinking always positive??

 

[Pythagorean]

Sure. It's just a matter of your coordinate system, really. Consider gravitational potential energy.

 

[pat666]

yeah i see that... so would the answer be "depends on the distance"? (i know I am just stabbing in the dark now but i need the answer and can't find anything useful in my textbook)

 

[Pythagorean]

let's take graphene's advice in post #2:

everything on the bottom you can hold constant (i.e. you can ignore it for this question)

r = distance. Distance is always positive in this case. It's the distance between the two charges (there's no way to make it negative, because the question of distance between two objects isn't concerned about the object's position relating to any coordinate system, just each other.)

So everything on the bottom is constant and positive. Now think of the different cases for q1 and q2 and what U they'll result in. Then use what you discover to answer the question.

 

[pat666]

if I am only concerned about the top then it has to be negative for this case doesn't it??

 

[Pythagorean]

Yup, like gravity, it will always be attractive. Opposite charges attract.