Griffiths Problem - Electrodynamics, Third Edition Problem 10.8 Confirm that the retarded potentials satisfy the Lorentz

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Griffiths Problem Electrodynamics Third Edition Problem 10 8 Confirm That The Retarded Potentials Satisfy The Lorentz 1 (54.41 KiB) Viewed 278 times

Griffiths Problem - Electrodynamics, Third Edition Problem 10.8 Confirm that the retarded potentials satisfy the Lorentz gauge condition. [Hint: First show that V. · · ( 1 ) = 2 / (V · J) + /- (V /² · J ) − v ². (V.J) • (-). where V denotes derivatives with respect to r, and V' denotes derivatives with respect to r'. Next, noting that J(r', 1-2/c) depends on r' both explicitly and through, whereas it depends on r only through, confirm that = —— J. (V₂), V' . J = −¡ — - | · 3= −p — — J. (♡'r) Use this to calculate the divergence of A (Eq. 10.19).] 1 p(r',t₁) но J(r', tr) V(r, t) = 47/480 [P(x²+4) dt', A(r. 1) = ; (10.19) Απε r 4л dt'.