- #1
sloneranger
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Hello,
I have a question regarding page 241 of “Principles of Electrodynamics” by Melvin Schwartz. He is deriving the electric field inside a conducting medium as a function of position z; by summing the incident field, contributions from slices of material to the left of z, and from slices to the right of z. I follow what he is doing (I think) up through calculating the first derivative of Ez. When taking the derivative of dEx/dz, he adds a term at the end of his expression for the second derivative that I don’t understand. The term is 4πσikEx(z) and it seems to come out of the blue (to me). Using the same math to get the second derivative as was used to calculate the first derivative, does not result in this term appearing. Please help me find what I am missing here; be it math and/or physics.
I have tried finding a similar derivation in other books without success. Later on the same page, Mr. Schwartz states that his derivation could be done much more rapidly by starting with Maxwell’s Equations and he then shows how this is done. His reason for the preceding derivation is to not, “lose the beautiful insight into the origin of the fields in terms of flowing currents.” Based on this and similar derivations from Maxwell’s Equations in other books, it seems that the term I don’t understand is real and necessary. I just don’t understand how he went from his expression for the first derivative to his results for the second derivative.
I would post the 2 equations, but I don’t know a good way to include the integral and exponential terms in this posting. If someone knows of a text that uses a similar approach to Schwartz’s, that may be all I need.
Thanks for your help!
sloneranger
I have a question regarding page 241 of “Principles of Electrodynamics” by Melvin Schwartz. He is deriving the electric field inside a conducting medium as a function of position z; by summing the incident field, contributions from slices of material to the left of z, and from slices to the right of z. I follow what he is doing (I think) up through calculating the first derivative of Ez. When taking the derivative of dEx/dz, he adds a term at the end of his expression for the second derivative that I don’t understand. The term is 4πσikEx(z) and it seems to come out of the blue (to me). Using the same math to get the second derivative as was used to calculate the first derivative, does not result in this term appearing. Please help me find what I am missing here; be it math and/or physics.
I have tried finding a similar derivation in other books without success. Later on the same page, Mr. Schwartz states that his derivation could be done much more rapidly by starting with Maxwell’s Equations and he then shows how this is done. His reason for the preceding derivation is to not, “lose the beautiful insight into the origin of the fields in terms of flowing currents.” Based on this and similar derivations from Maxwell’s Equations in other books, it seems that the term I don’t understand is real and necessary. I just don’t understand how he went from his expression for the first derivative to his results for the second derivative.
I would post the 2 equations, but I don’t know a good way to include the integral and exponential terms in this posting. If someone knows of a text that uses a similar approach to Schwartz’s, that may be all I need.
Thanks for your help!
sloneranger