What is Retarded time: Definition and 16 Discussions

In electromagnetism, electromagnetic waves in vacuum travel at the speed of light c, according to Maxwell's Equations. The retarded time is the time when the field began to propagate from the point where it was emitted to an observer. The term "retarded" is used in this context (and the literature) in the sense of propagation delays.

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  1. W

    Retarded time calculations: Electrodynamics

    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...
  2. L

    Retarded Green's Function for D'Alembertian

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

    Retarded Green's Function for D'Alembertian

    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## ...
  4. M

    Potential from a charge moving at constant velocity

    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...
  5. N

    Does Time Delay Affect the Curl of an Electric Field?

    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...
  6. genxium

    How to compute the divergence of retarded scalar potential

    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...
  7. M

    Full treatment of synchrotorn radiation

    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...
  8. E

    Implemented phase dispersion in retarded time

    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...
  9. L

    How to calculate the retarded time

    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...
  10. D

    Question about Retarded Time and Moving Charges

    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...
  11. F

    Calculation of an integral with retarded time

    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...
  12. N

    What is the Approximation for Retarded Time?

    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...
  13. Y

    How Does Retarded Time Change Between Static and Moving Charge Distributions?

    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...
  14. A

    Retarded Time & Position: Exploring Electrodynamic Concepts

    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...
  15. N

    Retarded Time Solutions for Non-Homogeneous Wave Equations

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

    Gradient equation with 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...