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## Main Question or Discussion Point

Hi, I have a doubt about a problem of classical electrodynamics (specifically for calculating the Lienard-Wiechert potentials).

(t_r is the retarded time, and t the time).

The position that has a particle is given by: x (t_r) = e cos (w t_r).

The squared modulus of the relative position vector is: R ^ 2 = r ^ 2 + x ^ 2 - 2rx

On the other hand, we know that: R ^ 2 = c ^ 2 (t-t_r) ^ 2

Equating the two expressions:

r ^ 2 + x ^ 2 - 2rx = c ^ 2 (t-t_r) ^ 2

Then, I have to replace x (t_r) and solve the equation for t_r, but I don't know how to solve it...maybe there's any trick for doing it.

Any idea?

Thank you.

(t_r is the retarded time, and t the time).

The position that has a particle is given by: x (t_r) = e cos (w t_r).

The squared modulus of the relative position vector is: R ^ 2 = r ^ 2 + x ^ 2 - 2rx

On the other hand, we know that: R ^ 2 = c ^ 2 (t-t_r) ^ 2

Equating the two expressions:

r ^ 2 + x ^ 2 - 2rx = c ^ 2 (t-t_r) ^ 2

Then, I have to replace x (t_r) and solve the equation for t_r, but I don't know how to solve it...maybe there's any trick for doing it.

Any idea?

Thank you.