Asked by lucca
1/2Eo times ( (volume integral)E^2 dtau + (surface integral)E PHI da )
That's the equation, the first integral is over the voume of a surface charged (q) sphere of radius a > R (radius of sphere) so a Gaussian surface beyond the sphere and the second is over the surface, with E vector function and PHI scalr function are the field and potential of q.
I believe this sum would show the total electrostatic energy, since if a => infinity the surface integral goes to zero (as stated in my book) but I'm not 100% sure nor do I know how to show it is really more/less than the total if I'm wrong. If someone can tell me which it is and how to go about proving it I think I can take it from there, just don't know how to start. Thanks!
Yes, you are integrating energy density over volume. That is total energy.
That's the equation, the first integral is over the voume of a surface charged (q) sphere of radius a > R (radius of sphere) so a Gaussian surface beyond the sphere and the second is over the surface, with E vector function and PHI scalr function are the field and potential of q.
I believe this sum would show the total electrostatic energy, since if a => infinity the surface integral goes to zero (as stated in my book) but I'm not 100% sure nor do I know how to show it is really more/less than the total if I'm wrong. If someone can tell me which it is and how to go about proving it I think I can take it from there, just don't know how to start. Thanks!
Yes, you are integrating energy density over volume. That is total energy.
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