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Forums
Physics
Classical Physics
The force from the energy gradient
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[QUOTE="user1139, post: 6794832, member: 680439"] [B]TL;DR Summary:[/B] Please see below From this post-[URL='https://physics.stackexchange.com/questions/690986/what-is-gradient-energy-in-classical-field-theory']gradient energy in classical field theory[/URL], one identifies the term ##E\equiv\frac{1}{2}\left(\partial_x\phi\right)^2## as the gradient energy which can be interpreted as elastic potential energy. Can one then say that $$F\equiv -\frac{\partial E}{\partial\left(\partial_x\phi\right)}=-\partial_x\phi$$ is the associated force? In addition, if one has the factor as ##2## instead of ##\frac{1}{2}##, can one just ignore the factor of ##4## and claim that the associated force is ##-\partial_x\phi## since the factor is just a scaling? [/QUOTE]
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Forums
Physics
Classical Physics
The force from the energy gradient
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