# Homework Help: Why is electric potential energy U defined negative in this example?

1. Oct 19, 2009

### The_Lobster

1. The problem statement, all variables and given/known data
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).

2. Relevant equations
In the solution of this problem, U is defined as
Code (Text):
U = -k e[SUP]^2[/SUP] / r
.

3. 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
Code (Text):
U = k e[SUP]^2[/SUP] / r
?

I'm feeling stupid right now! ;)

2. Oct 19, 2009

### Staff: Mentor

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.)

3. Oct 19, 2009

### The_Lobster

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

4. Oct 19, 2009

### Staff: Mentor

Note that U = 0 at r = ∞.

5. Oct 19, 2009

### The_Lobster

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

6. Oct 19, 2009

### Fightfish

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