# Quick question on potential

1. Jun 28, 2012

### cmmcnamara

Hi all,

So I do feel a bit silly with this question, but I've just begun to realize the relation ship between potential energy and potential functions....

So just quickly, would the following relationship be considered true:

$$\frac{d\vec{p}}{dt}=\nabla\phi$$

and by breaking apart the vectors, generally:

$$\frac{d\vec{p_s}}{dt}-\frac{d\phi}{ds}=0$$

Just wanted a quick verification and/or push in the right direction.

Thanks!

2. Jun 28, 2012

### Muphrid

Usually there's a negative sign in the first equation, because we define potential energy as decreasing along the direction of force. Otherwise, your logic is correct.

3. Jun 28, 2012

### cmmcnamara

I'm not sure I understand the negative sign, wouldn't that be dependent on the orientation of the force (eg, if my net force is pointed upwards from earth, potential energy increases with height).

4. Jun 28, 2012

### Muphrid

The gradient gives the direction of increase of a scalar field.

When the scalar field is potential energy, the force is always defined as the direction that potential energy decreases. Hence, a minus sign is required.