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(Electrostatics) Energy of a configuration 
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#1
Apr1409, 03:06 PM

P: 33

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


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