1) Show that the Liénard-Wiechert potentials given by Eqs. (10.46) and (10.47) properly satisfy the Lorentz gauge condit

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1 Show That The Lienard Wiechert Potentials Given By Eqs 10 46 And 10 47 Properly Satisfy The Lorentz Gauge Condit 1 (6.51 KiB) Viewed 35 times

1 Show That The Lienard Wiechert Potentials Given By Eqs 10 46 And 10 47 Properly Satisfy The Lorentz Gauge Condit 2 (18.94 KiB) Viewed 35 times

1 Show That The Lienard Wiechert Potentials Given By Eqs 10 46 And 10 47 Properly Satisfy The Lorentz Gauge Condit 3 (98.53 KiB) Viewed 35 times

1) Show that the Liénard-Wiechert potentials given by Eqs. (10.46) and (10.47) properly satisfy the Lorentz gauge condition given by Eq. (10.12).
pick The Lorenz gauge. In the Lorenz² gauge, we av V.A -Moto- = at (10.12)
It follows, then, that 1 qc V(r, t) = (10.46) 4лEо (rc - rv)' where v is the velocity of the charge at the retarded time, and is the vector from the retarded position to the field point r. Moreover, since the current density is pv (Eq. 5.26), the vector potential is p(r,tr)v(tr) но A(r, t) = Mo 4л form dt' { p(r, t,) dt', r 4л r or но qcv A(r, t) = = V(r,t). (10.47) 4π (rc - r. v) Equations 10.46 and 10.47 are the famous Liénard-Wiechert potentials for a moving point charge.15 = =