# (Electrostatics) Energy of a configuration

by LuisVela
Tags: configuration, electrostatics, energy
 P: 33 1. The problem statement, all variables and given/known data For a given configuration i found the scalar potential $$\phi(r)$$-->(as you can see its a function only of r) My question is about calculating the energy of the system. 2. Relevant equations $$W=-\dfrac{\varepsilon_0}{2}\int |\nabla \phi|^2 d^{3}x =\dfrac{1}{2}\int \phi \rho \,d^{3}x$$ 3. The attempt at a solution I just dont know if i should integrate $$\phi (r)$$ like a triple integral with limits $$(0,\infty)x(0,2\pi)x(0,\pi)$$ or should i perform the inverse substitution (from sferical coordinates to cartesian ) and then integrate $$\phi (x,y,z)$$ like a triple integral with limits (-oo,oo)x(-oo,oo)x(-oo,oo) Moreover, if i perform the change in the variables,what happen to the Jacobian of the substitution (|J|=$$r^2 sin(\vartheta)$$ )????

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