Retarded time Definition and 16 Threads

Homework Statement A positive charge ##q## is fired head-on at a distant positive charge ##Q## that is held stationary. It comes in at speed ##v_0## and comes to an instantaneous halt at distance ##r_f## away from Q. What is the amount of energy radiated due to acceleration in this time...

Hey All, I recently posted this in another area but was suggested to put it here instead. Here is my original post:

Homework Statement Hi all, I'm currently reviewing for a final and would like some help understanding a certain part of this particular problem: Determine the retarded Green's Function for the D'Alembertian operator ##D = \partial_s^2 - \Delta##, where ##\Delta \equiv \nabla \cdot \nabla## ...

Homework Statement Find the electric potential of a point charge with constant velocity ##v##. Homework Equations $$V(\mathbf{r}, t) = \frac{1}{4\pi\epsilon_0} \int \frac{\rho\left(\mathbf{r}', t - \frac{| \mathbf{r}- \mathbf{r}'| }{c}\right)}{| \mathbf{r}- \mathbf{r}'|}d^3r' $$ The Attempt...

I am thinking about the curl of the electric field and want to make sure I have something straight: Say you have a charged particle moving along some prescribed path. The electric field propagates outward at speed c, leading to a "retarded" time that you need to calculate in order to get the...

I'm learning time-dependent Maxwell's Equations and having difficulty understanding the following derivative: Given f(\textbf{r}, \textbf{r}', t) = \frac{[\rho(\textbf{r}, t)]}{|\textbf{r} - \textbf{r}'|} where \textbf{r} = x \cdot \textbf{i} + y \cdot \textbf{j} + z \cdot \textbf{k}, in...

Hello, I am trying to understand the details of the full treatment of synchrotron radiation. I am using Rybicki & Lightman (1979), along with the more detailed treatment given by Longair (1992). For instance, in Longair, chapter 18 (p.240 in the Second Edition), I see that the radiated energy...

Hi, I am trying to implement phase dispersion in a retarded time frame. c_{phase}(ω) = c_{0} + c'(ω) where c'(ω) is a small deviation from the reference phase speed c_{0}. In the frequency domain, the propagation term appears as an exponent: e^{-(\alpha + iω/c_{phase}(ω))z} where z is...

Homework Statement A charged particle is moving along the x-axis and its position is given by: \vec{r}'(t)=\sqrt{a^2+c^2t^2}\vec{e_x} I have to calculate the Lienard-Wiechert potentials, the electric and magnetic fields and the Poynting vector. Homework Equations...

I have a quick question about the retarded time when dealing with moving charges. The retarded time is: t' = t - \frac{r}{c} where r is the distance between the point of observation and the position of the charge. My question is very simple, is r a function of the normal time t , or...

Good morning. I would like to prove that the integral h^{\mu \nu} (\vec{r},t) = \int d \zeta \int d^3 \vec{y} \frac{F^{\mu \nu} (\zeta,\tilde{\tau}) \delta^{(3)} (\vec{r} - \vec{x}(\zeta,\tilde{\tau}))}{|\vec{r}-\vec{y}|} where \tilde{\tau} = t - |\vec{r}-\vec{y}|, is equal to \int...

Hello again! Facing some problems (my exam is taking place tomorrow... help is needed. Many thanks in advance!) I need to find an approximation for a retarded time. I don't understand how. This is what my lecturer wrote: sin(\varphi-\omega t)=exp(i\varphi'-i\omega(t-r/c)-i\omega(r'cos\theta...

This is regarding to derivative of retarded time t_r in static charge distribution vs moving charge distribution. t_r=t-\frac{\eta}{c} \;\hbox { where } \;\eta = \vec r - \vec w(t_r) \;\hbox { where } \vec r \;\hbox { is the stationary point where the potential is measured and } \vec...

Hey everyone, Just a quick question about a few electrodynamic concepts: 1) retarded time: t = t_r - (curly)r/c. Is t = total time, t_r = time elspased since the electromagnetic 'news' reached the point in question, and r/c = time taken to reach the point in question? 2) I'm a bit...

What is the significance of solutions to non-homogeneous wave equations for the scalar and vector potentials that utilize retarded time?

For a radiation problem, i am desperate about the expansion of the following equation: \nabla ( \hat{r} /r^2 \cdot \vec{p}(t_o)) where t_o is the retarded time at the center t_o=t-r/c and \vec{p}(t_o) is the electric dipole moment at t_o actually, it expands to 4 main parts and i am...