Directional Derivative of Potential energy

vgptgupta

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

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


I cannot understand what does "ij" indicate in "V_ij" and how does F=-∇_iV_ij. Why ∇_i, why not only ∇.

Please help anybody. I'm practically getting frustrated googling for answers.

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

mfb

i and j in V_ij 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.

vgptgupta

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

mfb

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

vgptgupta

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

jtbell

It means that the derivatives are with respect to x_i, y_i and z_i, not x_j, y_j and z_j.