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.
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...
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...
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...