Understanding Eq. 2.18 & Eq. 2.5 in Jackson's ED Book

  • Thread starter Thread starter rbwang1225
  • Start date Start date
  • Tags Tags
    Book
AI Thread Summary
In Jackson's Electrodynamics, Equation 2.18 and Equation 2.5 serve different purposes, which is a key point of confusion. Equation 2.5 is used to determine the surface charge for a given potential, while Equation 2.18 is applicable for the Dirichlet boundary condition using a Green's function. The differentiation in Equation 2.18 focuses on the position of the unit source, contrasting with Equation 2.5, which centers on the observation point. This distinction is crucial for understanding the context and application of each equation. Clarifying these differences can help navigate the complexities of this section in Jackson's text.
rbwang1225
Messages
112
Reaction score
0
In Jackson's ED book, he mentioned eq. 2.18 is essentially the same as eq. 2.5. What I don't understand is that in eq. 2.18 it is the position of the unit source to be differentiated while in eq. 2.5 it is the observation point. Is this O.K.?
 
Physics news on Phys.org
It might help if you provided the examples you were talking about. I know I don't have this book that you are referring to.
 
The two equations are for different things. That is why there are the two equations.
(2.5) is to get the surface charge for a given potential.
(2.18) is what is needed for the Dirichlet boundary condition using a GF.
That is one of the (many) difficult sections of J.
 
Last edited by a moderator:

Thread 'Off resonance driving of a MW/RF cavity'

Hello! Let's say I have a cavity resonant at 10 GHz with a Q factor of 1000. Given the Lorentzian shape of the cavity, I can also drive the cavity at, say 100 MHz. Of course the response will be very very weak, but non-zero given that the Loretzian shape never really reaches zero. I am trying to understand how are the magnetic and electric field distributions of the field at 100 MHz relative to the ones at 10 GHz? In particular, if inside the cavity I have some structure, such as 2 plates...
View full post »

Similar threads

Why is Hamilton's Principle assumed to be valid for non-holonomic systems?
Replies
25
Views
3K
I Atmospheric Density vs Altitude in an O'Neil Cylinder
Replies
1
Views
3K
A Dirac's "GTR" Eq (27.4): how momentum ##p^\mu## varies
2
Replies
50
Views
2K
A Quadrupole radiation formula for gravity
Replies
3
Views
1K
A Trying to understand couple stress in continua
Replies
6
Views
697
A Getting particle/antiparticle solutions from the Dirac Equation
Replies
6
Views
2K
How Do Controlled Sources Impact Thevenin Equivalent Calculations?
Replies
5
Views
2K
I Clarification required for some equations in the formulation of ideal Bose gas
Replies
2
Views
5K
B General Relativity, Twins & Schopenhauer: Analyzing Timing Diff.
Replies
18
Views
2K
A Equilibrium point of matter and radiation density
Replies
15
Views
2K

Hot Threads

Recent Insights

Back
Top