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Forums
Physics
Classical Physics
Gradient of a time-dependent function
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[QUOTE="Sturk200, post: 5674454, member: 557873"] Hi! I am struggling with what I think is probably a fairly simple step in Landau & Lifshitz derivation of the fields from the Lienard-Wiechert potential. We have the potential in terms of a primed set of coordinates but the fields are defined in terms of derivatives with respect to unprimed coordinates; the two are related by $$t'+{R(t')\over{c}} = t$$ where R is the distance from the point charge to the field point at time t' and time t is the moment of observation. The step that I am having trouble with is in finding an expression for the gradient of t'. Landau has: $$\nabla t' = -\frac{1}{c}\nabla R(t') = -\frac{1}{c} \bigg(\frac{\partial R}{\partial t'} \nabla t' + \frac{\textbf{R}}{R}\bigg)$$ The first equality obviously follows from the equation above. The second equality is where I am stumped. I would think that it should be simply $$\nabla R(t') = \frac{\partial R}{\partial t'} \nabla t'$$. Does anyone know where that extra unit vector term comes from? Thanks! [/QUOTE]
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Physics
Classical Physics
Gradient of a time-dependent function
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