Derivation/origin of two equations

  • Thread starter Thread starter thewall12
  • Start date Start date
AI Thread Summary
The discussion centers on two equations related to the scattering of electric fields and dipole moments. The first equation describes the amplitude of a scattered electric field, incorporating the dipole moment and the angle between the dipole and line of sight, but lacks clear literature references. The second equation for the scattered dipole moment suggests oscillation in space, raising questions about the nature of dipole oscillation, which is typically time-dependent. The user is seeking clarification on the origins and implications of these equations for their problem. Understanding these equations is crucial for grasping the underlying physics of dipole scattering.
thewall12
Messages
10
Reaction score
0
I've encountered two equations and I'm not sure of their origins. First, there's a differential equation describing the amplitude of a scattered electric field, E=(1/(c^2*r))*dp/dt sin y, where p is the scattered dipole moment and gamma (y) is the angle between the dipole moment and line of sight. The equation makes enough sense, I guess. I'm just not able to find any literature on it or its origin. Also, I'm not sure where the equation for the scattered dipole moment, p=po*exp(-ik(r-ct)), comes from. The r indicates that the dipole is oscillating in space, but if it's a dipole particle it can only oscillate in time, correct?
 
Physics news on Phys.org
Please help. I'm in desperate need of an answer for this problem I have.
 
Thread 'Gauss' law seems to imply instantaneous electric field propagation'

Thread 'Gauss' law seems to imply instantaneous electric field propagation'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
View full post »

Thread 'Do electron density waves accompany EM waves in coaxial cables?'

Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following transverse part $$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2} = \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$ and longitudinal part...
View full post »
Thread 'Recovering Hamilton's Equations from Poisson brackets'

Thread 'Recovering Hamilton's Equations from Poisson brackets'

The issue : Let me start by copying and pasting the relevant passage from the text, thanks to modern day methods of computing. The trouble is, in equation (4.79), it completely ignores the partial derivative of ##q_i## with respect to time, i.e. it puts ##\partial q_i/\partial t=0##. But ##q_i## is a dynamical variable of ##t##, or ##q_i(t)##. In the derivation of Hamilton's equations from the Hamiltonian, viz. ##H = p_i \dot q_i-L##, nowhere did we assume that ##\partial q_i/\partial...
View full post »

Similar threads

I Origin of coordinates in multipole expansion
Replies
10
Views
1K
Why is a current ring approx a magnetic dipole from very far off?
Replies
7
Views
2K
I Derivative of the retarded vector potential
Replies
1
Views
2K
Series expansion for 2D dipole displaced from the origin
Replies
1
Views
1K
I Physical Meaning of the Imaginary Part of a Wave Function
Replies
1
Views
2K
A Investigating the dielectric constant of a pure polar liquid
Replies
0
Views
2K
I Atmospheric Density vs Altitude in an O'Neil Cylinder
Replies
1
Views
3K
A Langevin equation - derivative of random force?
Replies
8
Views
2K
A Energy-to-angular momentum ratio in EM v. gravity quadrupole radiation
Replies
0
Views
1K
Permanent Dipole - Permanent Dipole Interaction Derivation
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top