Greetings,
I am trying to to show that the force in this form:
[itex]\dot{P}=e(\vec{∇}\vec{A})\vec{\dot{x}}-e\vec{∇}\phi[/itex]
Is equal to the lorentz force. I have been trying the approach of some sort of vector identity but have not gotten anywhere.
The equation and where I am trying to get with it are posted on wikipedia towards the bottom:
http://en.wikipedia.org/wiki/Hamiltonian_mechanics
I appreciate any help!
I am trying to to show that the force in this form:
[itex]\dot{P}=e(\vec{∇}\vec{A})\vec{\dot{x}}-e\vec{∇}\phi[/itex]
Is equal to the lorentz force. I have been trying the approach of some sort of vector identity but have not gotten anywhere.
The equation and where I am trying to get with it are posted on wikipedia towards the bottom:
http://en.wikipedia.org/wiki/Hamiltonian_mechanics
I appreciate any help!