- #1

lailola

- 46

- 0

## Homework Statement

A charged particle is moving along the x-axis and its position is given by: [itex]\vec{r}'(t)=\sqrt{a^2+c^2t^2}\vec{e_x}[/itex]

I have to calculate the Lienard-Wiechert potentials, the electric and magnetic fields and the Poynting vector.

## Homework Equations

[itex]\vec{A}=\frac{q\vec{v}}{cR-\vec{R}\vec{v}}[/itex]

[itex]\phi=\frac{qc}{cR-\vec{R}\vec{v}}[/itex]

(both evaluated in t_r)

with [itex]\vec{R}=\vec{r}-\vec{r}'(t_r)[/itex].

R=c(t-tr)

## The Attempt at a Solution

I have to find the retarded time tr to calculate the denominator of the potentials, and that is my doubt. I do:

[itex]R^2=(x-\sqrt{a^2+c^2t^2})^2+y^2+z^2[/itex]

[itex]R^2=c^2t_r^2+c^2t^2-2c^2tt_r[/itex]

Equating these two expressions I get tr but when I do it I get a horrible thing. It's an exam question so I think there will be another way to do this. Any idea?

Thank you