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Electrodynamics Nov 20, 2018
Quiz-VII
- Find the Green function \(g(x,x_0)\) satisfying the differential equation \[ \DD[g(x,x_0)]{x}=\delta(x-x_0) \] and obeying the boundary conditions \[ g(-L,x_0)=0; \qquad \qquad g(L,x_0)=0.\]
- A point charge \(q\) moves along a specified trajectory \(\vec{r}_0 (t)\) with velocity \(\vec{v}(t) = \dot{\vec{r}}_0 (t)\). For each choice of \(t\), show that the equation \(t' = t - |\vec{r} - \vec{r}_0(t')|/c\) has exactly one solution for the retarded time \(t'\), provided \(|\vec{v}(t)| < c\).\\[2mm] \null \hrulefill \paragraph*{Hint:} {\it Use reductio ad absurdum:} Assume two solutions \(t_1, t_2\) and derive a contradiction.\\ \FigNoNumX{10,30}{140}{100}{R-Time} This figure is part of the hint
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