Negative sign when finding forces from derivative of potential?

AI Thread Summary
When calculating forces from potential energy, the convention is to use F = -dV/dx, indicating that the force acts in the direction of decreasing potential. The negative sign signifies that forces tend to move systems toward lower potential energy states. This principle applies to various potentials, including Coulomb, gravitational, and harmonic potentials. Understanding the significance of the sign is crucial for correctly interpreting the direction of forces in physical systems. The discussion clarifies that the force direction is defined as negative when moving toward lower potential.
21joanna12
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Hi! I'm currently reading a book where they give the Coulomb potential, gravitational potential and harmonic potential as

+Q1Q2/4∏εx

-Gm1m2/x

+(1/2)qx2

I think I get the signs as they are used here, but when I am trying to find the force by taking the derivative of these with respect to x, I don't know whether to to f= +dV/dx or f= -dV/dx for any of them and I can't figure out the significance of the sign- which way is defined as +ve/-ve and why?

Sorry if I posted this is the wrong place or if it is not very clear :/ This is my first post of PF...

Thank you for any replies! :)
 
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F = -dV/dx

This way the force points "down" the slope to a lower potential.
 
Thank you! :)
 

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