Interaction Energy: What is W=\int dV $\rho(\vec{r}) \phi_{ext}(\vec{r})$?

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SUMMARY

The interaction energy is defined by the equation W=\int dV ρ(𝑟) φext(𝑟), which represents the energy required to move a charge distribution into an external potential from infinity. This equation is derived from the principles of electrostatics, where ρ(𝑟) denotes the charge density and φext(𝑟) signifies the external potential. Understanding this relationship is crucial for applications in electrostatics and potential theory.

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  • Understanding of electrostatics and potential energy concepts
  • Familiarity with charge density and its mathematical representation
  • Knowledge of integral calculus for evaluating the integral
  • Basic principles of field theory and potential functions
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Physicists, electrical engineers, and students studying electrostatics or potential theory will benefit from this discussion.

latentcorpse
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Hi. in my notes the interaction energy is simply stated as being

[itex]W=\int dV \rho(\vec{r}) \phi_{ext}(\vec{r})[/itex]
however no explanation is given as to where this comes from.
is it simply a fact or should i be able toderive this from somewhere?
 
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I think this essentially assumes you initially have an external potential phi, then this is the energy required to move the given charge distribution ito that potential from infinity
 

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