here are the two equations i'm dealing with:
Eq. 1: $$W=\frac{1}{2}\sum_{i=1}^n q_{i}V(r_{i})$$
Eq. 2: $$W=\frac{ε_{0}}{2}\int{E^{2}dT}$$
both equations describe the energy required to assemble a distribution of charges. (should go without saying that the first one is for point charge distributions, and the second one for continuous distributions)
i'm reading griffith's intro to electrodynamics and i don't understand the following:
An excerpt from ch. 2; he states: "Eq. 1 does not take into account the work necessary to make the point charge in the first place; we started with the point charges and simply found the work required to bring them together. This is a wise policy, since Eq. 2 indicates that the energy of a point charge is in fact infinite. Eq. 2 is more complete in the sense that it tells you the total energy stored in the charge configuration, but Eq. 1 is more appropriate when you're dealing with point charges, because we prefer to leave out that portion of the total energy that is attributable to the fabrication of the point charges themselves. In practice, after all, the point charges (electrons say) are given to us ready-made; all we do is move them around. Since we did not put them together and cannot take them apart it is immaterial how much work the process would involve. Still, the infinite energy of a point charge is a recurring source of embarrassment for electromagnetic theory, afflicting the quantum version as well as the classical."
I don't understand; are we referring to the energy required to actually create the electron? the energy stored in matter? i see no 'pc' terms, or anything of the like, anywhere in equation 2. it only has the work expressed in terms of the electric field, and volume. Where in the world did matter energy come into play?
Is this the only advantage eq. 2 has over eq. 1? that eq. 2 includes the 'total energy'?
Eq. 1: $$W=\frac{1}{2}\sum_{i=1}^n q_{i}V(r_{i})$$
Eq. 2: $$W=\frac{ε_{0}}{2}\int{E^{2}dT}$$
both equations describe the energy required to assemble a distribution of charges. (should go without saying that the first one is for point charge distributions, and the second one for continuous distributions)
i'm reading griffith's intro to electrodynamics and i don't understand the following:
An excerpt from ch. 2; he states: "Eq. 1 does not take into account the work necessary to make the point charge in the first place; we started with the point charges and simply found the work required to bring them together. This is a wise policy, since Eq. 2 indicates that the energy of a point charge is in fact infinite. Eq. 2 is more complete in the sense that it tells you the total energy stored in the charge configuration, but Eq. 1 is more appropriate when you're dealing with point charges, because we prefer to leave out that portion of the total energy that is attributable to the fabrication of the point charges themselves. In practice, after all, the point charges (electrons say) are given to us ready-made; all we do is move them around. Since we did not put them together and cannot take them apart it is immaterial how much work the process would involve. Still, the infinite energy of a point charge is a recurring source of embarrassment for electromagnetic theory, afflicting the quantum version as well as the classical."
I don't understand; are we referring to the energy required to actually create the electron? the energy stored in matter? i see no 'pc' terms, or anything of the like, anywhere in equation 2. it only has the work expressed in terms of the electric field, and volume. Where in the world did matter energy come into play?
Is this the only advantage eq. 2 has over eq. 1? that eq. 2 includes the 'total energy'?