Why is electric potential energy U defined negative in this example?

[The_Lobster]

Homework Statement

From Young and Freedman's book University Physics, ch 23, problem 23.54:
In the Bohr model of the hydrogen atom, a single electron revolves around a single proton in a circle of radius r. Assume the proton remains at rest. ++ (the rest is irrelevant to my question).

Homework Equations

In the solution of this problem, U is defined as

U = -k e[SUP]^2[/SUP] / r

.

The Attempt at a Solution

I've been staring at this equation for a long time. I'm probably just too tired. But why a minus in front of the equation? Why not just

U = k e[SUP]^2[/SUP] / r

?

I'm feeling stupid right now! ;)

Thank you in advance:)

 

[Doc Al]

The force is attractive--it requires work to move the electron away from the proton, thus the potential energy increases as r increases. Evaluate each expression at a few radii and see how the minus sign changes things.

(Compare a similar expression for gravitational potential energy.)

 

[The_Lobster]

Thank you very much for a fast and clear explanation! All confusion is gone:)

 

[Doc Al]

Note that U = 0 at r = ∞.

 

[The_Lobster]

Right right, so this electric potential energy would be analogous to a topographical "hole"... (?)

 

[Fightfish]

Yup, a potential well is the common analogy to such systems (gravitational etc.)