Say, we have potential energy of the form [itex]U = cos (\theta(t)) H(t)[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

H denotes a magnetic field that is time-dependent and it's an input variable to the system. Now when you take gradient of potential energy, would you write

[itex]\nabla U = \left[ - sin (\theta(t)) H(t) + cos (\theta(t)) \frac{\partial H(t)}{\partial \theta(t)}\right] \hat{e}_{\theta} = \left[ - sin (\theta(t)) H(t) + cos (\theta(t)) \frac{dH(t)/dt}{d\theta(t)/dt}\right] \hat{e}_{\theta}[/itex] ?

Should the 2nd term be present?

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# Gradient of a time-dependent potential energy

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