# Directional Derivative of Potential energy

1. Mar 11, 2013

### vgptgupta

I'm facing some problem in understanding few basic concepts of classical physics.

http://www.fotoshack.us/fotos/67357p0020-sel.jpg [Broken]

I cannot understand what does "ij" indicate in "Vij" and how does F=-∇iVij. Why ∇i, why not only ∇.

N.B. Equation 1.29
http://www.fotoshack.us/fotos/74847p0019-sel.jpg [Broken]

Last edited by a moderator: May 6, 2017
2. Mar 11, 2013

### Staff: Mentor

i and j in Vij are indices for particle numbers. As an example, V23 is the potential between particle 2 and particle 3.
$\nabla_i$ refers to the change of the position of particle i.

3. Mar 12, 2013

### vgptgupta

Thanks for the "ij" explanation but what about my other question i.e., why F=-∇iVij and why ∇i, why not only ∇.

4. Mar 12, 2013

### Staff: Mentor

There is no obvious meaning of ∇. Derivative for what?
What is meant here is the change in potential for particle i.

5. Mar 12, 2013

### vgptgupta

So what does the line "the subscript i on the del operator indicates that the derivatives are with respect to the components of ri" mean.

6. Mar 12, 2013

### Staff: Mentor

It means that the derivatives are with respect to xi, yi and zi, not xj, yj and zj.